Testing the Difference Between Two Means In Exercises 9–20, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) calculate
18. Pass Completion Percentages The pass completion percentages of 10 college football quarterbacks for their freshman and sophomore seasons are shown in the table below. At α = 0.10, is there enough evidence to support the claim that the pass completion percentages have changed? (Source: Sports Reference, LLC)
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Elementary Statistics: Picturing the World (7th Edition)
- Test the claim that the mean GPA of Orange Coast students is larger than the mean GPA of Coastline students at the 0.01 significance level. The null and alternative hypothesis would be: Ho:μο = μc Ho:μο με H1:po pc Hy:μο < με Reject the null hypothesis O Fail to reject the null hypothesis (to 2 decimals) (to 2 decimals)arrow_forward(a) Identify the claim and state H0 and Ha.What is the claim? Let Region A be sample 1 and let Region B be sample 2. Identify H0 and Ha. (b) Find the critical value(s) and identify the rejection region. What is the rejection region? (c) Find the standardized test statistic z. (d) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.arrow_forwardA hypothesis test result is considered to be statistically significant only when?arrow_forward
- Work Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 29, 50, 41, 29, 24. Use a 0.10 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? Click here to view the chi-square distribution table. The test statistic is. (Round to three decimal places as needed.) The critical value is (Round to three decimal places as needed.) State the conclusion. Ho- There sufficient evidence to support the claim that the outcomes are not equally likely. The outcomes to be equally likely, so the loaded die to behave differently from a fair die.arrow_forwardAnalysis of whether two categorical variables, X = course subject and Y = grade earned by a student was conducted. Researchers selected n = 800 students for their study using m = 4 distinct courses and k = 6 grades, from A to F and W. They evaluated a x2 test statistic for testing independence between X and Y equal to TS = 29.64 At the significance level a = 0.01, do researchers have sufficient evidence that X and Y are dependent? 1. Show critical value (or values) needed for this procedure 2. Formulate the rejection rule 3. State your decision: whether the independence hypothesis should be rejected at the significance level a = 0.01 Solutionarrow_forwardprovide an example of hypothesis testing using the t score testarrow_forward
- Explain the three types of t-tests (one-sample, two-sample independent and two-sample dependent t test) and include an example of each. What are the assumptions for using a two-sample independent t test?arrow_forwardTest the claim that the mean GPA of night students is significantly different than the mean GPA of day students at the 0.05 significance level. The null and alternative hypothesis would be: Ho: PNPD Ho: UN ≤ HD Ha:N HD Ha:μN > HD The test is: right-tailed two-tailed left-tailed O Ho: PNPD Ho: PNPD Ho: PN Ha:PN PD Oarrow_forwardTest the claim that the proportion of people who own cats is smaller than 80% at the 0.10 significance level. The null and alternative hypothesis would be: 0.8 Но: д — 0.8 Но:д 0.8 Но:р > 0.8 Нo:р H1: µ 0.8 H1:p > 0.8 The test is: left-tailed right-tailed two-tailed Based on a sample of 800 people, 73% owned cats The p-value is: (to 2 decimals) Based on this we: O Reject the null hypothesis Fail to reject the null hypothesisarrow_forward
- H0: p1=p2 H1: p1<p2 1) Identify the test statistic. 2)Identify the P-value.arrow_forwardTest the claim that the proportion of people who own cats is larger than 50% at the 0.05 significance level. The null and alternative hypothesis would be: Ho:u = 0.5 Ho:p 0.5 Ho:p > 0.5 H:p 0.5 H:p> 0.5 H1:p > 0.5 H1:p #0.5 H1:p < 0.5 H:p < 0.5 The test is: two-tailed left-tailed right-tailed Based on a sample of 500 people, 52% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Fail to reject the null hypothesis CO Reject the null hypothesis Check Answer op Carrow_forwardIdentify the claim and state Ho and H Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning. Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic. Decide whether to reject or fail to reject the null hypothesis. Interpret the decision in the context of the original claim. A hat company claims that the mean hat size for a male is at least 7.25. A random sample of 12 hat sizes has a mean of 7.15. At α = 0.01, can you reject the company’s claim? Assume the population is normally distributed and the population standard deviation is 0.27.arrow_forward
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