Statistics Questions & Answers

Describe type I and type II errors for a hypothesis test of the indicated claim. A shoe store claims that at least \( 30 \% \) of its new customers will return to buy their next pair of shoes. Describe the type I error. Choose the correct answer below. A. A type I error will occur when the actual proportion of new customers who return to buy their next pair of shoes is no more than 0.30 , but you reject \( H_{0}: p \leq 0.30 \). A type I error will occur when the actual proportion of new customers who return to buy their next pair of shoes is at least 0.30, but you reject \( H_{0}: p \geq 0.30 \). C. A type I error will occur when the actual proportion of new customers who return to buy their next pair of shoes is no more than 0.30 , but you fail to reject \( H_{0}: p \leq 0.30 \). D. A type I error will occur when the actual proportion of new customers who return to buy their next pair of shoes is at least 0.30 , but you fail to reject \( H_{0}: p \geq 0.30 \). Describe the type II error. Choose the correct answer below.

Find the P-value for the indicated hypothesis test with the given standardized test statistic, \( z \). Decide whether to reject \( \mathrm{H}_{0} \) for the given level of significance \( \alpha \). Right-tailed test with test statistic \( z=1.53 \) and \( \alpha=0.08 \) P-value \( =\square \) (Round to four decimal places as needed.) State your conclusion. Fail to reject \( \mathrm{H}_{0} \) Reject \( \mathrm{H}_{0} \)

A research center claims that more than \( 25 \% \) of employees in a certain country have changed jobs in the past three years. In a random sample of 260 people from that country, 78 have changed jobs in the past three years: At \( \alpha=0.05 \), is there enough evidence to support the center's claim? Complete parts (a) through (d) below. (b) Find the critical value(s) and identify the rejection region(s). Identify the critical value(s) for this test. \( z_{0}=\square \) (Round to two decimal places as needed. Use a comma to separate answers as needed.) Identify the rejection region(s). Select the correct choice below and fill in the answer box(es) to complete your choice. The rejection region is \( \square<z<\square \). (Round to two decimal places as needed.) B. The rejection regions are \( z<\square \) and \( z>\square \). C. The rejection region is \( z>\square \). D. The rejection region is \( z<\square \). (c) Find the standardized test statistic \( z \).

A research center claims that more than \( 25 \% \) of employees in a certain country have changed jobs in the past three years. In a random sample of 260 people from that country, 78 have changed jobs in the past three years At \( \alpha=0.05 \), is there enough evidence to support the center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state \( \mathrm{H}_{0} \) and \( \mathrm{H}_{\mathrm{a}} \). Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. The percentage of employees in the country who have changed jobs in the past three years is not B. More than \( \square \% \) of employees in the country have changed jobs in the past three years. D. At most \( \square \% \) of employees in the country have changed jobs in the past three years. Let p be the population proportion of successes, where a success is the country have changed jobs in the past three years. jobs in the past three years. State \( \mathrm{H}_{0} \) and \( \mathrm{H}_{\mathrm{a}} \). Select the correct choice below and fill in the answer boxes to complete vour choice.

Determine whether a normal sampling distribution can be used for the following sample statistics. If it can be used, test the claim about the difference between two population proportions \( p_{1} \) and \( p_{2} \) at the level of significance \( \alpha \). Assume that the samples are random and independent. Claim: \( p_{1} \neq p_{2}, \alpha=0.01 \) Sample Statistics: \( x_{1}=32, n_{1}=73, x_{2}=30, n_{2}=83 \) Calculate the standardized test statistic for the difference \( p_{1}-p_{2} \), if applicable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( z=\square \) B. The conditions to two decimal places as needed.) Calculate the \( P \)-value, if applicable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( p=\square \) (Round to three decimal places as needed.)

Determine whether a normal sampling distribution can be used for the following sample statistics. If it can be used, test the claim about the difference between two population proportions \( p_{1} \) and \( p_{2} \) at the level of significance \( \alpha \). Assume that the samples are random and independent. Claim: \( p_{1} \neq p_{2}, \alpha=0.01 \) Sample Statistics: \( x_{1}=32, n_{1}=73, x_{2}=30, n_{2}=83 \) Determine whether a normal sampling distribution can be used. The samples are random and independent. A normal sampling distribution \( n_{1} \bar{q}=\square, n_{2} \bar{p}=\square \), and \( n_{2} \bar{q}=\square \). (Round to two decimal places as needed.) State the null and alternative hypotheses, if applicable. A. \( H_{0}: p_{1}=p_{2} \) \( H_{a}: p_{1} \neq p_{2} \) B. \( H_{0}: p_{1} \geq p_{2} \) \( H_{a}: p_{1}<p_{2} \) C. \( H_{0}: p_{1} \leq p_{2} \) \( H_{a}: p_{1}>p_{2} \) D. The conditions to use a normal sampling distribution are not met.

For the following information, determine whether a normal sampling distribution can be used, where \( p \) is the population proportion, \( \alpha \) is the level of significance, \( \hat{p} \) is the sample proportion, and \( n \) is the sample size. If it can be used, test the claim. Claim: \( p \geq 0.47 ; \alpha=0.04 \). Sample statistics: \( \hat{p}=0.40, n=140 \) If a normal sampling distribution can be used, identify standardized test statistic \( z \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Round to two decimal places as needed.) B. A normal sampling distribution cannot be used. If a normal sampling distribution can be used, decide whether to reject or fail to reject the null hypothesis and interpret the decision. Choose the correct answer below. A. Reject the null hypothesis. There is not enough evidence to reject the claim. B. Fail to reject the null hypothesis. There is not enough evidence to reject the claim. C. Fail to reject the null hypothesis. There is enough evidence to reject the claim. D. Reject the null hypothesis. There is enough evidence to reject the claim. E. A normal samoling distrihution cannot he used

For the following information, determine whether a normal sampling distribution can be used, where \( p \) is the population proportion, \( \alpha \) is the level of significance, \( \hat{p} \) is the sample proportion, and \( n \) is the sample size. If it can be used, test the claim. Claim: \( p \geq 0.47 ; \alpha=0.04 \). Sample statistics: \( \hat{p}=0.40, n=140 \) Af a normal sampling distribution can be used, identify the critical value(s) for this test. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Round to two decimal places as needed. Use a comma to separate answers as needed.) B. A normal sampling distribution cannot be used. If a normal sampling distribution can be used, identify the rejection region(s). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The rejection region is \( z>\square \). (Round to two decimal places as needed.) B. The rejection region is \( \square<z<\square \). (Round to two decimal places as needed.)

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For the following information, determine whether a normal sampling distribution can be used, where \( p \) is the population proportion, \( \alpha \) is the level of significance, \( \hat{p} \) is the sample proportion, and \( n \) is the sample size. If it ca be used, test the claim. Claim: \( p \geq 0.47 ; \alpha=0.04 \). Sample statistics: \( \hat{p}=0.40, n=140 \) Let \( q=1-p \) and let \( \hat{q}=1-\hat{p} \). A normal sampling distribution \( \square \) can be used here, since If a normal sampling distribution can be used, identify the hypotheses for testing the claim. Select the correct ch