9. Hypothesis Testing for One Sample

When observed results are unlikely under the assumption that the null hypothesis is true, we say the result is _____and we reject the null hypothesis.

Discarded Plastic Data Set 42 “Garbage Weight” includes weights (pounds) of discarded plastic from 62 different households. Those 62 weights have a mean of 1.911 pounds and a standard deviation of 1.065 pounds. We want to use a 0.05 level of significance to test the claim that this sample is from a population with a mean less than 2.000 pounds. Identify the null hypothesis and alternative hypothesis.

Describe the test statistic for the sign test when the sample size n is less than or equal to 25 and when n is greater than 25.

Explain what “statistical significance” means.

In Exercises 1–5, (a) identify the claim and state H0 and Ha, (b) decide which nonparametric test to use, (c) find the critical value(s), (d) find the test statistic, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim.

[APPLET] A meteorologist wants to determine whether days with rain occur randomly in April in his hometown. To do so, the meteorologist records whether it rains for each day in April. The results are shown, where R represents a day with rain and N represents a day with no rain. At , can the meteorologist conclude that days with rain are not random?

N R R N N N N R N R R N R R R

N R R R R N N N N R N R N N R

Performing a Runs Test In Exercises 15 – 20, (b) find the critical values. Use α = 0.05

Coin Toss A coach records the results of the coin toss at the beginning of each football game for a season. The results are shown, where H represents heads and T represents tails. The coach claimed the tosses were not random. Test the coach’s claim.

H T T T H T H H T T T T H T H H

Premature Birth and Education Does the length of term of pregnancy play a role in the level of education of the baby? Researchers in Norway followed over 1 million births between 1967 and 1988 and looked at the educational attainment of the children. The following data are based on the results of their research. Note that a full-term pregnancy is 38 weeks. Is gestational period independent of completing a high school diploma? Use the α = 0.05 level of significance.

Hypotheses and Conclusions Refer to the hypothesis test described in Exercise 1.

a. Identify the null hypothesis and the alternative hypothesis.

Writing Hypotheses: Internet Provider An Internet provider is trying to gain advertising deals and claims that the mean time a customer spends online per day is greater than 28 minutes. You are asked to test this claim. How would you write the null and alternative hypotheses when

b. you represent a competing advertiser and want to reject the claim?

Discarded Plastic The P-value for the hypothesis test described in Exercise 1 is 0.2565.

What should be concluded about the null hypothesis?

What is the final conclusion that addresses the original claim?

"[DATA] Height versus Head Circumference [See Problem 13 in Section 12.3] A pediatrician wants to determine the relation that may exist between a child’s height and head circumference. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the following data:

b. Suppose the researcher wanted to determine if there is a positive association between height and head circumference. What would be the null and alternative hypotheses?"

In Exercises 1–10, use the following weights (g) of Hershey’s Kisses from Data Set 38 “Candies” in Appendix B.

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tTest The bag of Hershey’s Kisses includes 75 of the candies. According to the label, the total weight is 340 g, so the candies should have a mean weight of 340/75 = 4.5333 g. Use the sample of weights listed above to test the claim that they are from a population with a mean of 4.5333 g. Use a 0.05 significance level with a t test. What does the conclusion suggest about the claim of 340 g printed on the label?

In Exercises 1–10, use the following weights (g) of Hershey’s Kisses from Data Set 38 “Candies” in Appendix B.

Sign Test Repeat Exercise 3 using the sign test to test the claim that the sample of weights is from a population with a median of 4.5333 g.

Interpreting a P-Value In Exercises 3–8, the P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a)α=0.01, (b) α=0.05 , and (c) α=0.10.

P = 0.0838

Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.

Base Price of an ATV The standard deviation of the base price of an all-terrain vehicle is no more than \$320.