Question 1

11eb4928_20e6_85f2_b114_7bc9d3b7c519_TB7192_00

Accepted Answer

The test statistic is calculated using the formula for a proportion z-test: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{136}{400} = 0.34$, $p_0 = 0.28$, and $n = 400$. Plugging these values into the formula gives $z = 2.67$, indicating that the problem of making mortgage payments is more severe in these cities compared to the national average.

Question 2

11eb4928_20e6_5ee0_b114_cd8797b149d1_TB7192_00

Accepted Answer

The $P$-value for $t \geq 1.76$ with 17 degrees of freedom is closest to $0.0482$, which can be found using $t$-distribution tables or statistical software.

Question 3

11eb4928_20e6_ad04_b114_eb323ae2d30f_TB7192_00

Accepted Answer

B

Question 4

A manufacturer claims that the mean amount of juice in its 16 ounce bottles are 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the
Mean amount is actually less than this.

A)Lower-tailed
B)Two-sided
C)Upper-tailed

Accepted Answer

The hypothesis test is looking to see if the mean amount is less than the claimed value of 16.1 ounces, indicating a lower-tailed test.

Question 5

A pharmaceutical company wants to answer the question whether it takes longer than 45 seconds for a drug in pill form to dissolve in the gastric juices of the stomach.A sample was
Taken from patients taking the given drug in pill form and times for the pills to be dissolved
Were measured.State assumptions of the test.
I)The subjects must be part of a medical study group investigating the drug.
II)The subjects in the sample must be randomly selected from a population.
III)The sample data must come from a normally distributed population of observations for
The variable under study.

A)I only
B)II only
C)III only
D)II and III
E)None of these

Accepted Answer

The correct assumptions for the test include that the subjects in the sample must be randomly selected from a population (to ensure representativeness) and that the sample data must come from a normally distributed population of observations for the variable under study (a common assumption for many statistical tests, especially when dealing with means). Being part of a medical study group is not a necessary assumption for the statistical test itself, although it might be relevant for other aspects of research design.

Question 6

11eb4928_20e6_ad06_b114_43f9d60404fa_TB7192_00

Accepted Answer

The $P$-value for $t \geq -1.47$ with 21 degrees of freedom is the area to the right of $t = -1.47$ on a $t$-distribution with 21 degrees of freedom. This area represents the probability of observing a value as extreme as or more extreme than $t = -1.47$. Since $t$-distributions are symmetric, and the given $t$ value is negative, we're looking for the upper tail area corresponding to the positive side of the distribution. The $P$-value is therefore large, indicating a high probability of observing such a value by chance, which aligns with option C, $0.9218$.

Question 7

11eb4928_20e6_ad05_b114_f33d4e34a605_TB7192_00

Accepted Answer

The null hypothesis ($H_0$) typically states there is no effect or no difference, and it is usually the hypothesis that the researcher wants to test against. Here, the researcher claims the proportion ($p$) is less than $5\%$, so the null hypothesis should state the proportion is equal to $5\%$, as we assume the status quo until evidence suggests otherwise. The alternative hypothesis ($H_A$) should represent the researcher's claim, which is $p < 0.05$. Therefore, the correct hypotheses are $H_0: p = 0.05, H_A: p < 0.05$.

Question 8

11eb4928_20e6_37cf_b114_9f1a3459e39f_TB7192_00

Accepted Answer

The null hypothesis ($H_0$) typically represents a statement of no effect or no difference, or the status quo, which in this case is that 17% of male fireflies are unable to produce light due to a genetic mutation ($p = 0.17$). The alternative hypothesis ($H_A$) represents what the researcher is trying to prove, which is that fewer than 17% of male fireflies are unable to produce light ($p < 0.17$).

Question 9

11eb4928_20e6_85f1_b114_cf71b8cd1cf6_TB7192_00

Accepted Answer

The null hypothesis ($H_0$) typically represents the status quo or a statement of no effect, which in this case is that the proportion ($p$) of Americans having difficulty making mortgage payments is 0.28, as reported for the general U.S. population. The alternative hypothesis ($H_A$) is what the study aims to test against the null hypothesis. Since the question is whether the problem is more severe in the sampled cities, the alternative hypothesis should suggest that the proportion is greater than 0.28, making the correct choice $H_0: p = 0.28$ and $H_A: p > 0.28$.

Question 10

The owner of a football team claims that the average attendance at games is over 74,900, and he is therefore justified in moving the team to a city with a larger stadium.An independent
Investigator will conduct a hypothesis test to determine whether his claim is accurate.

A)Lower-tailed
B)Upper-tailed
C)Two-sided

Accepted Answer

The hypothesis test is upper-tailed because the owner claims the average attendance is over a specific value (74,900), which implies testing for values greater than this threshold.

Question 11

Data in 1980 showed that about 40% of the adult population had never smoked cigarettes.In 2004, a national health survey interviewed a random sample of 2000 adults and found that
50% had never been smokers.Create a 95% confidence interval for the proportion of adults
(in 2004) who had never been smokers.

A)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 52.2%.
B)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 37.4% and 52.2%.
C)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 58.2%.
D)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 40% and 60%.
E)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 63.2%.

Accepted Answer

The answer of Data in 1980 showed that about 40%...

Question 12

Using the t-tables, software, or a calculator, estimate the critical value of t for the given confidence interval and degrees of freedom: 99% confidence interval with df = 24&#10;A)2.492&#10;B)2.797&#10;C)2.807&#10;D)2.779&#10;E)1.711

Accepted Answer

The answer of Using the t-tables, software, or a calculator,...

Question 13

11eb4928_20e6_10be_b114_7330b2381247_TB7192_00

Accepted Answer

The answer of 11eb4928_20e6_10be_b114_7330b2381247_TB7192_00...

Question 14

11eb4928_20e6_85f3_b114_2168fc7b6f31_TB7192_00

Accepted Answer

The answer of 11eb4928_20e6_85f3_b114_2168fc7b6f31_TB7192_00...

Question 15

11eb4928_20e6_fb27_b114_235ef3732454_TB7192_00

Accepted Answer

The answer of 11eb4928_20e6_fb27_b114_235ef3732454_TB7192_00...

Question 16

The manufacturer of a refrigerator system produces refrigerators that are supposed to maintain a true mean temperature, μ, of 48°F, ideal for certain beverages.The owner of a
Beverage company does not agree with the refrigerator manufacturer, and will conduct a
Hypothesis test to determine whether the true mean temperature differs from this value.

A)Two-sided
B)Upper-tailed
C)Lower-tailed

Accepted Answer

The answer of The manufacturer of a refrigerator system produces...

Question 17

In the past, the mean running time for a certain type of flashlight battery has been 8.5 hours. The manufacturer has introduced a change in the production method and wants to perform a
Hypothesis test to determine whether the mean running time has changed as a result.

A)Lower-tailed
B)Upper-tailed
C)Two-sided

Accepted Answer

The answer of In the past, the mean running time...

Deck 18: Testing Hypotheses