Question 1

Traditionally in hypothesis testing the null hypothesis represents the "status quo" which will be overturned only if there is evidence against it. Which of the statements below might represent a
Null hypothesis? 
A)The teaching method raises SAT scores.
B)The treatment has no effect.
C)The defendant is guilty.
D)None of the above

Accepted Answer

The null hypothesis typically states there is no effect or no difference, which matches option B: "The treatment has no effect." This aligns with the traditional approach of assuming no change or effect until evidence suggests otherwise.

Question 2

Provide an appropriate response.
-Suppose that you wish to perform a hypothesis test for a population mean using the critical value method. The test is right-tailed. Suppose that the population standard deviation is unknown. The correct procedure to use is the t-test. If you mistakenly use the standard normal table to obtain the critical value, will the value that you obtain be larger or smaller than the correct value? Does the mistaken use of the normal table make it more or less likely that the null hypothesis will be rejected?

Accepted Answer

The critical value obtained using the standard normal table will be smaller than the correct critical value. This will make it more likely that the null hypothesis will be rejected.

Question 3

Provide an appropriate response.
-A right-tailed hypothesis test for a population mean is to be performed. If the null hypothesis is rejected at the 5% level of significance, does this necessarily mean that it would be rejected at the 1% level of significance? at the 10% level of significance? Explain your reasoning. In your explanation, refer to the critical values corresponding to the different significance levels.

Accepted Answer

A null hypothesis which is rejected at the 5% level of significance will certainly be rejected at the 10% level of significance but not necessarily at the 1% level of significance. If the null hypothesis is rejected at the 5% level of significance, the test statistic is greater than the critical value of 1.645. This means that the test statistic is certainly greater than 1.28 which is the critical value corresponding to a 10% level of significance. The test statistic is not necessarily greater than 2.33 which is the critical value corresponding to a 1% level of significance.

Question 4

A hypothesis test for a population mean is to be performed. The hypotheses are 
$\begin{array} { l } 
\mathrm { H } _ { 0 } : \mu = 106 \
\mathrm { H } _ { \mathrm { a } } : \mu < 106 .
\end{array}$
Which of the sketches below could represent the power curve for the test? 
A)

B)

C)

D)

Accepted Answer

The answer of A hypothesis test for a population mean...

Question 5

A high school biology student wishes to test the hypothesis that hummingbird feeders can affect the mean mass of ruby-throated hummingbirds in the area surrounding the feeder. She captures And weighs several of the hummingbirds near a science museum where several feeders are located. She obtains the following masses in grams: $\begin{array} { l l l l l l } 4.4 & 3.9 & 4.5 & 4.3 & 4.1 & 3.8 \ 3.8 & 4.1 & 3.9 & 3.8 & 3.2 & 4.3 \end{array}$ $\begin{array} { l l l l l l } 3.8 & 4.1 & 3.9 & 3.8 & 3.2 & 4.3 \end{array}$ The student's hypotheses are: $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 3.65 \mathrm {~g} \ \mathrm { H } _ { \mathrm { a } } : \mu > 3.65 \mathrm {~g} \end{array}$$ Use technology to calculate the P-value, then determine whether the data provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. Test at the $5 \%$ significance level and assume that the population standard deviation is $0.35 \mathrm {~g}$. Also, assess the strength of the evidence against the null hypothesis. A)$\mathrm { P } = 0.0004$; since $\mathrm { P } < 0.05$, reject the null hypothesis. At the $5 \%$ significance level, the data do provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. The evidence against the null hypothesis is very strong. B) $\mathrm { P } = 0.0002$; since $\mathrm { P } < 0.05$, reject the null hypothesis. At the 5\% significance level, the data do provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. The evidence against the null hypothesis is very strong. C) $P = 0.9998$; since $P > 0.05$, do not reject the null hypothesis. At the $5 \%$ significance level, the data do not provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. The evidence against the null hypothesis is weak or none. D) $\mathrm { P } = 0.0004$; since $\mathrm { P } < 0.05$, do not reject the null hypothesis. At the $5 \%$ significance level, the data do not provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. The evidence against the null hypothesis is weak or none.

Accepted Answer

The answer of A high school biology student wishes to...

Question 6

Perform a hypothesis test for the population mean. Assume that preliminary data analyses indicate that it is reasonable toapply the z-test. Use the critical-value approach.
-A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600 mg claimed by the manufacturer. Test this claim at the 2% level of significance. The mean acetaminophen content for a random sample of n = 48 tablets is 605 mg. Assume that the population standard deviation is 4.8 mg.

Accepted Answer

The answer of Perform a hypothesis test for the population...

Question 7

Decide whether it appears reasonable to use a t-test to perform a hypothesis test for the mean in question. Explain youranswer and include any relevant graphs, such as a normal probability plot, histogram, or stem-and-leaf diagram. If thereare outliers, explain how to proceed.
-Test scores for a random sample of 12 students were as follows: $\begin{array} { l c c c c c }  22 & 30 & 34 & 37 & 40 & 45 \ 49 & 53 & 58 & 65 & 74 & 87 \end{array}$

Accepted Answer

The answer of Decide whether it appears reasonable to use...

Question 8

Provide an appropriate response.
-A man is on trial accused of murder in the first degree. The prosecutor presents evidence that he hopes will convince the jury to reject the hypothesis that the man is innocent. This situation can be modeled as a hypothesis test with the following hypotheses: $\mathrm { H } _ { 0 }$ : The defendant is innocent. $\mathrm { H } _ { \mathrm { a } }$ : The defendant is guilty. If convicted, the defendant will receive the death penalty. Do you think that a Type I error or a Type II error would be more serious? Why?

Accepted Answer

The answer of Provide an appropriate response.
-A man is on...

Question 9

Perform a one-sample z-test for a population mean using the P-value approach. Be sure to state the hypotheses and thesignificance level, to compute the value of the test statistic, to obtain the P-value, and to state your conclusion. Also,assess the strength of the evidence against the null hypothesis.
-In one city, the average amount of time that tenth-graders spend watching television each week is 21.6 hours. The principal of Birchwood High School believes that at his school, tenth-graders watch less television. For a sample of 28 tenth-graders from Birchwood High School, the mean amount of time spent watching television per week was 19.4 hours. Do the data provide sufficient evidence to conclude that for tenth-graders at Birchwood High School, the mean amount of time spent watching television per week is less than the city average of 21.6 hours? Perform the appropriate hypothesis test using a significance level of 5%. Assume that $$\sigma$$ = 7.2 hours.

Accepted Answer

The answer of Perform a one-sample z-test for a population...

Question 10

A high school biology student wishes to test the hypothesis that hummingbird feeders can affect the mean mass of ruby-throated hummingbirds in the area surrounding the feeder. She captures
And weighs several of the hummingbirds near a science museum where several feeders are located. She obtains the following masses in grams: $$\begin{array} { l l l l l l } 
4.2 & 3.9 & 3.6 & 3.5 & 3.9 & 3.8 \
3.8 & 4.1 & 3.9 & 3.8 & 3.2 & 3.4
\end{array}$$ The student's hypotheses are:
$\mathrm { H } _ { 0 } : \mu = 3.65 \mathrm {~g}$
$\mathrm { H } _ { \mathrm { a } } : \mu > 3.65 \mathrm {~g}$
Use technology to calculate the P-value, then determine whether the data provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. Test at the $5 \%$ significance level and assume that the population standard deviation is $0.35 \mathrm {~g}$. Also, assess the strength of the evidence against the null hypothesis.  
A)$\mathrm { P } = 0.745$; since $\mathrm { P } > 0.05$, do not reject the null hypothesis.
At the $5 \%$ significance level, the data do not provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. The evidence against the null hypothesis is weak or none.
B) $\mathrm { P } = 0.255$; since $\mathrm { P } > 0.05$, reject the null hypothesis.
At the $5 \%$ significance level, the data do provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. The evidence against the null hypothesis is moderate.
C) $\mathrm { P } = 0.509$; since $\mathrm { P } > 0.05$, reject the null hypothesis.
At the $5 \%$ significance level, the data do provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. The evidence against the null hypothesis is strong.
D) $\mathrm { P } = 0.1418$; since $\mathrm { P } > 0.05$, do not reject the null hypothesis.
At the $5 \%$ significance level, the data do not provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. The evidence against the null hypothesis is weak or none.

Accepted Answer

The answer of A high school biology student wishes to...

Question 11

Provide an appropriate response.
-Give an example of a hypothesis test for which it is important to have a small β probability. Explain why it is important to have a small value for $\beta .$

Accepted Answer

The answer of Provide an appropriate response.
-Give an example of...

Question 12

Provide an appropriate response.
-For a fixed sample size, how will increasing the significance level of a hypothesis test affect the probability of a Type I error? How will it affect the probability of a Type II error?

Accepted Answer

The answer of Provide an appropriate response.
-For a fixed sample...

Question 13

Construct a graph portraying the decision criterion for the specified hypothesis test.
-A hypothesis test for a population mean is conducted. The hypotheses are:  $\begin{array} { l }  \mathrm { H } _ { 0 } : \mu = \mu _ { 0 } \ \mathrm { H } _ { \mathrm { a } } : \mu > \mu _ { 0 } \end{array}$  The significance level is 0.04 and the critical value is 1.75. Sketch a normal curve displaying the decision criterion. This curve will represent the normal curve for the test statistic under the assumption that the null hypothesis is true. On your graph indicate the area in the tail, the critical value, the rejection region, and the nonrejection region.

Accepted Answer

The answer of Construct a graph portraying the decision criterion...

Question 14

Two graphical displays are given for a set of data. A hypothesis test is to be performed for the mean of the populationfrom which the data were obtained. Would it be reasonable to use a one-mean z-test? Explain your reasoning. Assumethat the population standard deviation is known.
-A normal probability plot and a stem-and-leaf diagram of the data are given below.  $$\begin{array} { l | l }  2 & 2 \ 3 & 047 \ 4 & 059 \ 5 & 38 \ 6 & 5 \ 7 & 4 \ 8 & 7 \end{array}$$

Accepted Answer

The answer of Two graphical displays are given for a...

Question 15

Solve the problem. Use the critical-value approach.
-A hypothesis test for a population mean is to be performed. If the sample size is small (less than 15), under what conditions is it reasonable to use the z-test? If the sample size is moderate (between 15 and 30), under what conditions is it reasonable to use the z-test?

Accepted Answer

The answer of Solve the problem. Use the critical-value approach.
-A...

Question 16

Construct a graph portraying the decision criterion for the specified hypothesis test.
-In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours)between failures.  $\begin{array} { l l l l l }  518 & 548 & 561 & 523 & 536 \ 499 & 538 & 557 & 528 & 563 \end{array}$  At the 5% significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours.

Accepted Answer

The answer of Construct a graph portraying the decision criterion...

Question 17

Solve the problem. Use the critical-value approach.
-A sheet-metal press stamps out bolt washers with a nominal inner diameter of 0.25 inches. Measurement of the inner diameters of a random sample of 14 washers produced the following Results (in inches): 
$\begin{array} { l l l l l l l } 
0.253 & 0.251 & 0.253 & 0.251 & 0.264 & 0.252 & 0.259 \
0.252 & 0.264 & 0.263 & 0.253 & 0.268 & 0.266 & 0.268
\end{array}$ 
The normal scores of the data are summarized below: 
Using technology, perform the following hypothesis test: at the $1 \%$ significance level, determine whether the mean washer diameter for this machine exceeds the nominal value. Comment on the appropriateness of the test.  
A)Test statistic: $t = 2.6503$; Critical value: $4.5865$.
Since the test statistic is less than the critical value, do not reject the null hypothesis $\mathrm { H } _ { 0 } : \mu = 0.25$ inches. There is insufficient evidence to conclude that the inner diameter is larger than the nominal value. However, the normal probability plot indicates that the data are not distributed normally, so the t-test may not be appropriate. 
B) Test statistic: $t = 2.6503$; Critical value: $4.5865$.
Since the test statistic is less than the critical value, do not reject the null hypothesis
$\mathrm { H } _ { 0 } : \mu = 0.25$ inches. There is insufficient evidence to conclude that the inner diameter is larger than the nominal value. The normal probability distribution plot indicates that the t-test is an appropriate test.
C) Test statistic: $t = 4.5865$; Critical value: $1.7709$.
Since the test statistic is greater than the critical value, reject the null hypothesis $\mathrm { H } _ { 0 } : \mu = 0.25$ inches.
There is sufficient evidence to conclude that the inner diameter is larger than the nominal value. However, the normal probability plot indicates that the data are not distributed normally, so the t-test may not be appropriate.
D) Test statistic: $t = 4.5865$; Critical value: $2.650$.
Since the test statistic is greater than the critical value, reject the null hypothesis $\mathrm { H } _ { 0 } : \mu = 0.25$ inches.
There is sufficient evidence to conclude that the inner diameter is larger than the nominal value. However, the normal probability plot indicates that the data are not distributed normally, so the t-test may not be appropriate.

Accepted Answer

The answer of Solve the problem. Use the critical-value approach.
-A...

Question 18

Solve the problem. Use the critical-value approach.
-A machine that fills soda bottles is supposed to fill them to a mean volume of 16.2 fluid ounces. A random sample of 20 filled bottles produced the following volumes in fluid ounces: $$\begin{array}{l}
\begin{array} { l l l l l l l l l l } 
16.3 & 15.9 & 16.7 & 15.3 & 17.1 & 16.4 & 3.9 & 15.9 & 16.2 & 3.4 \
16.4 & 8.2 & 15.5 & 16.5 & 16.0 & 16.3 & 15.8 & 16.7 & 16.5 & 15.5
\end{array}\
\text { These data are summarized on the following histogram: }
\end{array}$$

Using technology, perform the following hypothesis test: at the 5% significance level,determine Whether the fill volume is less than the supposed value. Comment on the appropriateness of the Test. 
A) Test statistic: $t = - 1.8063$; Critical value: $- 2.0921$.
Since the test statistic is greater than the critical value, do not reject the null hypothesis $\mathrm { H } _ { 0 } : \mu = 16.2 \mathrm { oz }$. There is insufficient evidence to conclude that the fill volume is below $16.2$ oz. The conclusion is on sound statistical ground.
B) Test statistic: $t = - 1.8063$; Critical value: $- 1.7254$.
Since the test statistic is less than the critical value, do not reject the null hypothesis $\mathrm { H } _ { 0 } : \mu =$ $16.2 \mathrm { oz }$.
There is insufficient evidence to conclude that the fill volume is below $16.2$ oz. However, the data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.
C) Test statistic: $t = - 1.8063$; Critical value; $- 2.0921$.
Since the test statistic is greater than the critical value, do not reject the null hypothesis $\mathrm { H } _ { 0 } : \mu = 16.2 \mathrm { oz }$. There is insufficient evidence to conclude that the fill volume is below $16.2$
oz. However, the data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.
D) Test statistic: $t = - 1.8063$; Critical value: $- 1.729$.
Since the test statistic is less than the critical value, reject the null hypothesis $\mathrm { H } _ { 0 } : \mu = 16.2 \mathrm { oz }$.
There is sufficient evidence to conclude that the fill volume is below $16.2 \mathrm { oz }$. However, the data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.

Accepted Answer

The answer of Solve the problem. Use the critical-value approach.
-A...

Question 19

Provide an appropriate response.
-Suppose that you want to perform a hypothesis test for a population mean. Give an example of a situation in which both the z-test and the Wilcoxon signed-rank test are permissible but the Wilcoxon signed-rank test is preferable. Specify the distribution of the variable under consideration, the sample size, and whether or not the population standard deviation is known.

Accepted Answer

The answer of Provide an appropriate response.
-Suppose that you want...

Question 20

A hypothesis test for a population mean is to be performed. The hypotheses are 
$\begin{array} { l } 
\mathrm { H } _ { 0 } : \mu = 100 \
\mathrm { H } _ { \mathrm { a } } : \mu > 100
\end{array}$ 
Which of the sketches below could represent the power curve for the test? 
A)

B)

C)

D)

Accepted Answer

The answer of A hypothesis test for a population mean...

Quiz 9: Hypothesis Tests for One Population Mean

Traditionally in hypothesis testing the null hypothesis represents the "status quo" which will be overturned only if there is evidence against it. Which of the statements below might represent a Null hypothesis?

A hypothesis test for a population mean is to be performed. The hypotheses are $\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 106 \\\mathrm { H } _ { \mathrm { a } } : \mu < 106 .\end{array}$ Which of the sketches below could represent the power curve for the test?

Provide an appropriate response. -Give an example of a hypothesis test for which it is important to have a small β probability. Explain why it is important to have a small value for $\beta .$

Provide an appropriate response. -For a fixed sample size, how will increasing the significance level of a hypothesis test affect the probability of a Type I error? How will it affect the probability of a Type II error?

A hypothesis test for a population mean is to be performed. The hypotheses are $\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 100 \\\mathrm { H } _ { \mathrm { a } } : \mu > 100\end{array}$ Which of the sketches below could represent the power curve for the test?

Quiz 9: Hypothesis Tests for One Population Mean

Traditionally in hypothesis testing the null hypothesis represents the "status quo" which will be overturned only if there is evidence against it. Which of the statements below might represent a Null hypothesis?

Provide an appropriate response. -Give an example of a hypothesis test for which it is important to have a small β probability. Explain why it is important to have a small value for β.\beta .β.

Provide an appropriate response. -For a fixed sample size, how will increasing the significance level of a hypothesis test affect the probability of a Type I error? How will it affect the probability of a Type II error?

Provide an appropriate response. -Give an example of a hypothesis test for which it is important to have a small β probability. Explain why it is important to have a small value for $\beta .$