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- The graduation rate from high school in a certain county is 76%. A school in that county wants to know if its graduation rate is significantly lower than the county rate. They take a random sample of 300 of the seniors who graduated last year, and find that 223 out of those 300 graduated. What set of hypotheses should be tested in this case?A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percentage. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level.NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. H0: plocal ≠ pnational H0: plocal > pnational H0: plocal = pnational H0: plocal < pnational Part (b) State the alternative hypothesis. Ha: plocal < pnational Ha: plocal = pnational Ha: plocal ≠ pnational Ha: plocal > pnational…To study whether the students at a university are more or less satisfied with the current food service compared to the previous food service, a sample of 93 current students is taken and finds that 40 are satisfied with the current food service. A similar survey was taken for the previous food service in which 82 students surveyed found that 41 were satisfied with the previous food service. When testing the hypothesis (at the 5% level of significance) a higher percentage of students were satisfied with the previous food service than with the current food service, what is the test statistic? (please round your answer to 2 decimal places)
- In a recent study, 100 males used a new weight-loss supplement, and 70 of them experienced weight loss after two weeks. In the same study, 20 females used the same supplement, and 15 of them experienced weight loss after two weeks. Fill in the blanks below to make the most reasonable statement possible. The new weight-loss supplement was less effective on (Choose one) to lose weight after two weeks, whereas only % of the (Choose one) in the study. That is because of them failed failed to lose weight after two weeks. X ŚA doctor used to believe that babies were equally likely to be born any day of the week, but with the rise in scheduled deliveries, the doctor now claims that babies are twice as likely to be born on a weekday (Monday through Friday) than on a weekend (Saturday and Sunday). To test this theory, she selects a random sample of 120 babies born this year and determines on which day of the week they were born. She finds that 4 were born on Sunday, 24 on Monday, 21 on Tuesday, 18 on Wednesday, 22 on Thursday, 28 on Friday, and 3 on Saturday. She would like to carry out a test of significance to test her claim. What is the value of the chi-square test statistic and the P-value of this test? Find the chi-square table here. χ2 = 12.95, P-value is between 0.025 and 0.05 χ2 = 12.95, P-value is between 0.05 and 0.10 χ2 = 28.74, P-value is less than 0.0005 χ2 = 28.74, P-value is between 0.0005 and 0.0013.) In a randomized experiment, double-blind clinical trials of Prevnar, infants were randomly divided into twogroups. Subjects in group 1 received Prevnar, while subjects in group 2 received a control vaccine. After the seconddose, 137 of 452 subjects who received Prevnar experienced drowsiness as a side effect. After the second dose, 31of 99 subjects who the control vaccine experienced drowsiness as a side effect. Does the evidence suggest that alower proportion of subjects who took Prevnar experienced drowsiness as a side effect than subjects who had thecontrol vaccine at the ? = 0.01 level of significance?a.) Verify that the requirements for inference about two population proportions is satisfied.b.) What is the Null and Alternative Hypotheses? What test will you be using?c.) What is the level of significance and the ?-value?
- Is this the correct answer?A teacher is comparing the mena study time of his freshmen and senior students. He believes that his senior students spend more time studyin per week than his freshmen studnet and decides to perform a hypothesis test on his belief. a. Suppose the decision of the hypothesis test is to reject the null hypothesis. If, in realiry, treshmen study for a mean of 10 hours per week and seniors study for a mena of 15 hours per week, was an error made? if so, what type? b. Suppose the decision of the hypothesis test is to fail to reject the null hypothesis. if, in realiry, freshmen study for a mena of 15 hours per seek and seniors study for a mean of 15 hours per week, was an error made? is so, what type?A salesman for a new manufacturer of cellular phones claims not only that they cost the retailer less but also that the percentage of defective cellular phones found among his products, ( p1 ), will be no higher than the percentage of defectives found in a competitor's line, ( p2 ). To test this statement, the retailer took a random sample of 130 of the salesman's cellular phones and 110 of the competitor's cellular phones. The retailer found that 10 of the salesman's cellular phones and 5 of the competitor's cellular phones were defective. Does the retailer have enough evidence to reject the salesman's claim? Use a significance level of α=0.05 for the test. Step 4 of 6 : Compute the value of the test statistic. Round your answer to two decimal places.
- Suppose a drug company designs to develop a new drug to prevent colds. The companystates that the drug is equally effective for men and women. To test this claim, theychoose a simple random sample of 100 women and 200 men from a population of100,000 volunteers.At the end of the study, 38 women caught a cold; and 102 men caught a cold. (a) Based on these findings, can we reject the company's claim that the drug is equallyeffective for men and women? Use a 0.05 level of significance. (b) Find the 95% confidence interval for the difference between the proportions ofwomen and men caught a cold. (c) Are the results of (a) and (b) consistent? Explain brieflyThe contingency table shows the result of a random sample of students by Lika Salmanyan at PCC and the number of hours they spend investing on Robinhood and Acorns by age and gender. At alpha =0.05, can you conclude that age is related to gender when it comes to time spent investing on Robinhood and Acorns. Gender 16-20yrs 21-30yrs 31-40yrs 41-50yrs 51-60yrs 61yrs or older Male 45 170 90 72 45 26 Female 9 30 21 17 10 5 What are the degrees of freedom? What is the critical value? Leave your answers in 3 decimal places The degrees of freedom is and the P- value is .The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 10.7% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. (a) Explain why this is a binomial experiment.
