Question 1

Test Hypotheses about a Population Mean with Unknown
-Find the standardized test statistic t for a sample with n = 10, x = 8.8, s = 1.3, and = 0.05 if H0: 9.7. Round your answer to three decimal places.

Accepted Answer

The standardized test statistic $t$ is calculated using the formula $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean under the null hypothesis, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values: $t = \frac{8.8 - 9.7}{(1.3/\sqrt{10})} = -2.189$, rounded to three decimal places.

Question 2

Test Hypotheses about a Population Mean with Known Using P-values
-A local company claims that the number of days missed by its employees due to illness is below the national average of 5 . A random sample of 40 employees provided the data below. At $\alpha = 0.05$, test the company's claim using $\mathrm { P }$-values.
$\begin{array} { c c c c c c c c c c } 0 & 3 & 6 & 3 & 3 & 5 & 4 & 1 & 3 & 5 \ 7 & 3 & 1 & 2 & 3 & 3 & 2 & 4 & 1 & 6 \ 2 & 5 & 2 & 8 & 3 & 1 & 2 & 5 & 4 & 1 \ 1 & 1 & 2 & 1 & 5 & 7 & 5 & 4 & 9 & 3 \end{array}$

Accepted Answer

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Question 3

Test Hypotheses about a Population Mean with Known Using Confidence Intervals
-A group of 40 homeowners showed that their average monthly gasoline bill was $\$ 192$ with a standard deviation of $\$ 8$. According to a national consumer group, their mean bill should be $\mu = \$ 188$. Test this hypothesis by constructing a $95 \%$ confidence interval for the population mean.

Accepted Answer

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Question 4

Test Hypotheses about a Population Mean with Known Using Confidence Intervals
-When testing $\mathrm { H } _ { 0 } : \mu = \mu _ { 0 }$, using confidence intervals, if $\mu$ is not contained in the confidence interval then we would

Accepted Answer

When $\mu$ (the population mean) is not contained within the confidence interval, it suggests that the hypothesized mean $\mu_0$ is not likely to be the true population mean, leading to the rejection of the null hypothesis $\mathrm { H } _ { 0 }$.

Question 5

Test Hypotheses about a Population Mean with Known Using Confidence Intervals
-In a random sample of 60 digital cameras, the mean repair cost was $\$ 150$ with a standard deviation of $\$ 36$. A local repairman claims that the mean cost of repair should be $\$ 165$. Test this hypothesis by constructing a $99 \%$ confidence interval for the population mean.

Accepted Answer

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Question 6

Test Hypotheses about a Population Mean with Unknown
-Find the standardized test statistic $t$ for a sample with $\mathrm { n } = 25 , \overline { \mathrm { x } } = 19 , \mathrm {~s} = 3$, and $\alpha = 0.005$ if $\mathrm { H } _ { 1 } : \mu > 18$. Round your answer to three decimal places.

Accepted Answer

The standardized test statistic $t$ is calculated using the formula $t = \frac{\overline{x} - \mu}{s / \sqrt{n}}$, where $\overline{x}$ is the sample mean, $\mu$ is the population mean under the null hypothesis, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values, $t = \frac{19 - 18}{3 / \sqrt{25}} = \frac{1}{3 / 5} = \frac{5}{3} = 1.667$.

Question 7

Test Hypotheses about a Population Mean with Unknown
-Find the standardized test statistic t for a sample with $\mathrm { n } = 20 , \bar { x } = 11.2 , \mathrm {~s} = 2.0$, and $\alpha = 0.05$ if $\mathrm { H } _ { 1 } : \mu < 11.6$. Round your answer to three decimal places.

Accepted Answer

The standardized test statistic $t$ is calculated using the formula $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $\mu$ is the population mean under the null hypothesis. Plugging in the given values: $t = \frac{11.2 - 11.6}{(2.0/\sqrt{20})}$ results in $t \approx -0.894$.

Question 8

Test Hypotheses about a Population Mean with Known Using P-values
-If the level of significance is $0.05$, and the $\mathrm { P }$-value is $0.043$, the decision would be to

Accepted Answer

Since the P-value (0.043) is less than the level of significance (0.05), the decision would be to reject the null hypothesis ($H_0$).

Question 9

Test Hypotheses about a Population Mean with Known Using P-values
-A bank claims that the mean waiting time in line is less than $3.9$ minutes. A random sample of 60 customers has a mean of $3.8$ minutes with a standard deviation of $0.6$ minute. If $\alpha = 0.05$, test the bank's claim using $\mathrm { P }$-values.

Accepted Answer

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Question 10

Test Hypotheses about a Population Mean with Known Using Confidence Intervals
-A random sample of 56 lithium batteries has a mean life of 645 hours with a standard deviation of 31 hours. A leading consumer journal states that the mean life for these batteries is $\mu = 639$ hours. Test this hypothesis by constructing a $95 \%$ confidence interval for the population mean.

Accepted Answer

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Question 11

Distinguish between Statistical Significance and Practical Significance
-True or False: Results that are statistically significant are always practically significant.

Accepted Answer

Statistical significance refers to the likelihood that a result is not due to chance, based on a statistical test, while practical significance considers whether the size of the effect is large enough to be of interest in real-world applications. A result can be statistically significant without being practically significant if the effect size is too small to matter in practical scenarios.

Question 12

Test Hypotheses about a Population Mean with Unknown
-Find the standardized test statistic $t$ for a sample with $\mathrm { n } = 15 , \overline { \mathrm { x } } = 10.8 , \mathrm {~s} = 0.8$, and $\alpha = 0.05$ if $\mathrm { H } _ { 0 } : \mu \leq 10.5$. Round your answer to three decimal places.

Accepted Answer

The correct answer is A because the standardized test statistic $t$ is calculated as:$$t = \frac{\overline{x} - \mu_0}{s/\sqrt{n}} = \frac{10.8 - 10.5}{0.8/\sqrt{15}} = 1.452$$

Question 13

Test Hypotheses about a Population Mean with Unknown
-Find the standardized test statistic t for a sample with $\mathrm { n } = 12 , \overline { \mathrm { x } } = 15.2 , \mathrm {~s} = 2.2$, and $\alpha = 0.01$ if $\mathrm { H } _ { 0 } : \mu = 14$. Round your answer to three decimal places.

Accepted Answer

The standardized test statistic $t$ is calculated using the formula $t = \frac{\overline{x} - \mu}{s / \sqrt{n}}$, where $\overline{x}$ is the sample mean, $\mu$ is the population mean under the null hypothesis, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values, $t = \frac{15.2 - 14}{2.2 / \sqrt{12}} \approx 1.890$.

Question 14

Test Hypotheses about a Population Mean with Known Using P-values
-What is a P-value?

Accepted Answer

A P-value is the probability of observing a sample statistic (or one more extreme) assuming that the null hypothesis is true. It measures the strength of evidence against the null hypothesis.

Question 15

Test Hypotheses about a Population Mean with Unknown
-$$\text { Use a t-test to test the claim } \mu \geq 13 \text { at } \alpha = 0.05 \text {, given the sample statistics } \mathrm { n } = 10 , \overline { \mathrm { x } } = 12.1 \text {, and } \mathrm { s } = 1.3 \text {. }$$

Accepted Answer

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Question 16

Test Hypotheses about a Population Mean with Known Using P-values
-Given $\mathrm { H } _ { 0 } : \mu \leq 85 , \mathrm { H } _ { 1 } : \mu > 85$, and $\mathrm { P } = 0.006$. Do you reject or fail to reject $\mathrm { H } _ { 0 }$ at the $0.01$ level of significance?

Accepted Answer

Since the p-value (0.006) is less than the significance level (0.01), we reject the null hypothesis $\mathrm { H } _ { 0 }$.

Question 17

Test Hypotheses about a Population Mean with Unknown
-Find the standardized test statistic t for a sample with $\mathrm { n } = 12 , \overline { \mathrm { x } } = 18.5 , \mathrm {~s} = 2.1$, and $\alpha = 0.01$ if $\mathrm { H } _ { 1 } : \mu \neq 19$. Round your answer to three decimal places.

Accepted Answer

The standardized test statistic $t$ is calculated using the formula $t = \frac{\overline{x} - \mu}{(s/\sqrt{n})}$, where $\overline{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $\mu$ is the population mean under the null hypothesis. Plugging in the given values, $t = \frac{18.5 - 19}{(2.1/\sqrt{12})}$ results in $t \approx -0.825$.

Question 18

Test Hypotheses about a Population Mean with Unknown
-$$\text { Use a t-test to test the claim } \mu = 24 \text { at } \alpha = 0.01 \text {, given the sample statistics } \mathrm { n } = 12 , \overline { \mathrm { x } } = 25.2 \text {, and } \mathrm { s } = 2.2 \text {. }$$

Accepted Answer

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Question 19

Test Hypotheses about a Population Mean with Known Using Confidence Intervals
-A group of 49 randomly selected construction workers has a mean age of $22.4$ years with a standard deviation of $3.8$. According to a recent survey, the mean age should be $\mu = 21.9$ years. Test this hypothesis by constructing a $98 \%$ confidence interval for the population mean.

Accepted Answer

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Question 20

Distinguish between Statistical Significance and Practical Significance
-True or False: Results that are practically significant will always be statistically significant.

Accepted Answer

Statistical significance refers to the likelihood that a result is not due to chance, while practical significance considers if the size of the effect is large enough to be meaningful in real-world situations. Results can be statistically significant without being practically significant if the effect size is very small.

Quiz 10: Hypothesis Tests Regarding a Parameter

Test Hypotheses about a Population Mean with Unknown -Find the standardized test statistic t for a sample with n = 10, x = 8.8, s = 1.3, and = 0.05 if H0: 9.7. Round your answer to three decimal places.

Test Hypotheses about a Population Mean with Known Using Confidence Intervals -When testing $\mathrm { H } _ { 0 } : \mu = \mu _ { 0 }$ , using confidence intervals, if $\mu$ is not contained in the confidence interval then we would

Test Hypotheses about a Population Mean with Unknown -Find the standardized test statistic $t$ for a sample with $\mathrm { n } = 25 , \overline { \mathrm { x } } = 19 , \mathrm {~s} = 3$ , and $\alpha = 0.005$ if $\mathrm { H } _ { 1 } : \mu > 18$ . Round your answer to three decimal places.

Test Hypotheses about a Population Mean with Unknown -Find the standardized test statistic t for a sample with $\mathrm { n } = 20 , \bar { x } = 11.2 , \mathrm {~s} = 2.0$ , and $\alpha = 0.05$ if $\mathrm { H } _ { 1 } : \mu < 11.6$ . Round your answer to three decimal places.

Test Hypotheses about a Population Mean with Known Using P-values -If the level of significance is $0.05$ , and the $\mathrm { P }$ -value is $0.043$ , the decision would be to

Distinguish between Statistical Significance and Practical Significance -True or False: Results that are statistically significant are always practically significant.

Test Hypotheses about a Population Mean with Unknown -Find the standardized test statistic t for a sample with $\mathrm { n } = 12 , \overline { \mathrm { x } } = 15.2 , \mathrm {~s} = 2.2$ , and $\alpha = 0.01$ if $\mathrm { H } _ { 0 } : \mu = 14$ . Round your answer to three decimal places.

Test Hypotheses about a Population Mean with Known Using P-values -What is a P-value?

Test Hypotheses about a Population Mean with Unknown - $\text { Use a t-test to test the claim } \mu \geq 13 \text { at } \alpha = 0.05 \text {, given the sample statistics } \mathrm { n } = 10 , \overline { \mathrm { x } } = 12.1 \text {, and } \mathrm { s } = 1.3 \text {. }$

Test Hypotheses about a Population Mean with Known Using P-values -Given $\mathrm { H } _ { 0 } : \mu \leq 85 , \mathrm { H } _ { 1 } : \mu > 85$ , and $\mathrm { P } = 0.006$ . Do you reject or fail to reject $\mathrm { H } _ { 0 }$ at the $0.01$ level of significance?

Test Hypotheses about a Population Mean with Unknown -Find the standardized test statistic t for a sample with $\mathrm { n } = 12 , \overline { \mathrm { x } } = 18.5 , \mathrm {~s} = 2.1$ , and $\alpha = 0.01$ if $\mathrm { H } _ { 1 } : \mu \neq 19$ . Round your answer to three decimal places.

Test Hypotheses about a Population Mean with Unknown - $\text { Use a t-test to test the claim } \mu = 24 \text { at } \alpha = 0.01 \text {, given the sample statistics } \mathrm { n } = 12 , \overline { \mathrm { x } } = 25.2 \text {, and } \mathrm { s } = 2.2 \text {. }$

Distinguish between Statistical Significance and Practical Significance -True or False: Results that are practically significant will always be statistically significant.

Quiz 10: Hypothesis Tests Regarding a Parameter

Test Hypotheses about a Population Mean with Unknown -Find the standardized test statistic t for a sample with n = 10, x = 8.8, s = 1.3, and = 0.05 if H0: 9.7. Round your answer to three decimal places.

Test Hypotheses about a Population Mean with Known Using Confidence Intervals -When testing H0:μ=μ0\mathrm { H } _ { 0 } : \mu = \mu _ { 0 }H0​:μ=μ0​ , using confidence intervals, if μ\muμ is not contained in the confidence interval then we would

Test Hypotheses about a Population Mean with Known Using P-values -If the level of significance is 0.050.050.05 , and the P\mathrm { P }P -value is 0.0430.0430.043 , the decision would be to

Distinguish between Statistical Significance and Practical Significance -True or False: Results that are statistically significant are always practically significant.

Test Hypotheses about a Population Mean with Known Using P-values -What is a P-value?

Distinguish between Statistical Significance and Practical Significance -True or False: Results that are practically significant will always be statistically significant.

Test Hypotheses about a Population Mean with Known Using Confidence Intervals -When testing $\mathrm { H } _ { 0 } : \mu = \mu _ { 0 }$ , using confidence intervals, if $\mu$ is not contained in the confidence interval then we would

Test Hypotheses about a Population Mean with Known Using P-values -If the level of significance is $0.05$ , and the $\mathrm { P }$ -value is $0.043$ , the decision would be to