Chapter 6 Course Pack - MATH 1340

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MATH 1340 Chapter 6: Hypothesis Tests 1 of 8 Section 6.1: Basics of Hypothesis Tests Ex 1) State the null and alternative hypotheses in a statistical hypothesis test involving the given claim. Then determine if the test is left-tailed, right-tailed, or two-tailed. (a) A restaurant claims that at least 80% of the items on its menu are made only from certified organic ingredients. (b) The President claims that the average age of people collecting unemployment benefits is 43.8 years. (c) A store claims that its customers save an average of more than $10 for every $100 they spend at their store compared to a competitor. Ex 2) Assume that a hypothesis test is to be conducted, and the test statistic is z or t (so the sampling distribution is bell-shaped). (a) If a left-tailed test in conducted at the 0.01 significance level, sketch the sampling distribution of the test statistic and label the shaded area above the rejection region. (b) If a two-tailed test with = 0.1 is conducted, sketch the sampling distribution of the test statistic and label the shaded area above the rejection region. (c) If the rejection region of a test is under both tails of the test statistic’s density curve, and the area under each tail that is above the corresponding rejection region is 0.02, sketch the sampling distribution of the test statistic and label the shaded area above the rejection region. What is the significance level of this test? Ex 3) A hypothesis test of the following claim is to be conducted: “the average time that a customer waits for his/her food to be served after placing an order is less than 15 minutes.” A random sample of 47 customer orders is selected, and it yields a test statistic of t = -1.31. A significance level of 0.05 is to be used. (a) Conduct this hypothesis test using the critical value method. (b) Conduct this hypothesis test using the P -value method.
MATH 1340 Chapter 6: Hypothesis Tests 2 of 8 (c) State the final conclusion of this hypothesis test in nontechnical language that addresses the original claim. (d) If the true population mean waiting time is 14.2 minutes, then identify whether a type I error, a type II error, or a correct decision was made. Ex 4) A hypothesis test of the following claim is to be conducted: “the average attack percentage per game for the Monarchs’ volleyball team is 0.297.” (“Attack percentage” in volleyball is the number of kills minus the number of hitting errors, all divided by the total number of attacks). A random sample of 35 of their games is selected, and it yields a test statistic of t = 2.27. A significance level of 0.1 is to be used. (a) Conduct this hypothesis test using the critical value method. (b) Conduct this hypothesis test using the P -value method. (c) State the final conclusion of this hypothesis test in nontechnical language that addresses the original claim. (d) If the true average attack percentage per game is 0.305, then identify whether a type I error, a type II error, or a correct decision was made. Ex 5) A hypothesis test of the following claim is to be conducted: “the percentage of currently enrolled students who are required to take Elementary Statistics is more than 75%.” A random sample of 101 students is selected, and it yields a test statistic of z = 2.30. A significance level of 0.02 is to be used. (a) Conduct this hypothesis test using the critical value method. (b) Conduct this hypothesis test using the P -value method.
MATH 1340 Chapter 6: Hypothesis Tests 3 of 8 (c) State the final conclusion of this hypothesis test in nontechnical language that addresses the original claim. (d) If the true percentage of students required to take Elementary Statistics is 73.6%, then identify whether a type I error, a type II error, or a correct decision was made. Section 6.2: Hypothesis Tests Involving a Single Proportion Ex 6) In a random sample of 50 registered voters from Pleasantville, it was found that 27 of them voted in the previous city council election. The mayor of Pleasantville claims that at least 60% of the city’s registered voters actually did vote in the election. What is the value of the test statistic that would be used in a test of this claim? Ex 7) A survey of 561 customers of Save-Mart revealed that 58% of them have used the store’s mobile app at least once. The manager of the IT department for Save-Mart claims that more than 55% of customers have used the app. Find the value of the test statistic that would be use in a test of this claim. Ex 8) A geneticist claimed that less than 7.5% of fish given a specific growth hormone gene would incorporate it into their DNA. Scientists injected this gene into thousands of fish eggs. Of the 400 fish that grew from these eggs, 20 of them incorporated the gene into their DNA. Test the geneticist’s claim at the 0.05 significance level.
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