91影视

Fair coin? You want to determine if a coin is fair. So you toss it $10$times and record the proportion of tosses that land 鈥渉eads.鈥� You would like to perform a test of $H_0:p=0.5$versus $H_a:p鈮�0.5$, where $p$= the proportion of all tosses of the

coin that would land 鈥渉eads.鈥� Check if the conditions for performing the significance test are met.

Home computersRefer to Exercise 35.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and $P$-value.

c. What conclusion would you make?

AttitudesThe Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' attitudes toward school and study habits. Scores range from 0 to 200 . Higher scores indicate better attitudes and study habits. The mean score for U.S. college students is about 115. A teacher suspects that older students have better attitudes toward school, on average. She gives the SSHA to an SRS of 45 of the over 1000 students at her college who are at least 30 years of age.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

Walking to school Refer to Exercise 36.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and $P$-value.

c. What conclusion would you make?

Significance tests A test of $H_o:p=0.5$versus $H_a:p>0.5$based on

a sample of size $200$yields the standardized test statistic $z=2.19$. Assume that the conditions for performing inference are met.

a. Find and interpret the P-value.

b. What conclusion would you make at the $伪=0.01$ significance level? Would

your conclusion change if you used 伪=0.05 instead? Explain your reasoning.

c. Determine the value of p^= the sample proportion of successes.

Significance tests A test of $H_0:p=0.65$ against $H_a:p<0.65$

based on a sample of size $400$ yields the standardized test statistic $z=鈭�1.78$ .

a. Find and interpret the $P$-value.

b. What conclusion would you make at the $伪=0.10$ significance level? Would

your conclusion change if you used $伪=0.05$ instead? Explain your reasoning.

c. Determine the value of $\stackrel{铃�}{p}$= the sample proportion of successes.

Bullies in middle school A media report claims that more than $75\%$of

middle school students engage in bullying behavior. A University of Illinois study on aggressive behavior surveyed a random sample of $558$middle school students. When asked to describe their behavior in the last $30$days, $445$students admitted that they had engaged in physical aggression, social ridicule, teasing, name-calling, and issuing threats 鈥攁ll of which would be classified as bullying. Do these data provide convincing evidence at the $伪=0.05$significance level that the media report鈥檚 claim is correct?

Watching grass grow The germination rate of seeds is defined as the proportion of seeds that sprout and grow when properly planted and watered. A certain variety of grass seed usually has a germination rate of $0.80$. A company wants to see if spraying the seeds with a chemical that is known to increase germination rates in other species will increase the germination rate of this variety of grass. The company researchers spray a random sample of $400$grass seeds with the chemical, and $339$of the seeds germinate. Do these data provide convincing evidence at the $伪=0.05$ significance level that the chemical is

effective for this variety of grass?

Better parking A local high school makes a change that should improve student

satisfaction with the parking situation. Before the change, $37\%$of the school鈥檚 students approved of the parking that was provided. After the change, the principal surveys an SRS of $200$from the more than $2500$students at the school. In all, $83$students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Is there convincing evidence that the principal鈥檚 claim is true?

Side effects A drug manufacturer claims that less than $10\%$of patients who take its new drug for treating Alzheimer鈥檚 disease will experience nausea. To test this claim, researchers conduct an experiment. They give the new drug to a random sample of $300$out of $5000$Alzheimer鈥檚 patients whose families have given informed consent for the patients to participate in the study. In all, $25$of the subjects experience nausea.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Do these data provide convincing evidence for the drug manufacturer鈥檚 claim?