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
17. Product Ratings A company claims that its consumer product ratings (0–10) have changed from last year to this year. The table shows the company’s product ratings from the same eight consumers for last year and this year. At α = 0.05, is there enough evidence to support the company’s claim?
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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_forwardTest the claim that the proportion of people who own cats is larger than 20% at the 0.005 significance level. The null and alternative hypothesis would be: H2:p = 0.2 Họ:p 2 0.2 H9:p 0.2 H9:p = 0.2 Hg: u 0.2 H1: u 0.2 The test is: left-tailed two-tailed right-tailed Based on a sample of 300 people, 24% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesisarrow_forward
- A hypothesis test result is considered to be statistically significant only when?arrow_forwardWork 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_forward
- provide an example of hypothesis testing using the t score testarrow_forwardExplain 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_forward
- Test the claim that the proportion of people who own cats is larger than 10% at the 0.10 significance level.The null and alternative hypothesis would be: H0:p=0.1 Ha:p>0.1 The test is right tailed Based on a sample of 300 people, 14% owned catsThe test statistic is: (to 2 decimals)The p-value is: (to 2 decimals)arrow_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_forwardH0: p1=p2 H1: p1<p2 1) Identify the test statistic. 2)Identify the P-value.arrow_forward
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