10.20 Internet Usage In 2018 Pew Research reported that 11% of Americans do not use the Internet. Suppose in a random sample of 200 Americans, 26 reported not using the Internet. Using a chi-square test for goodness-of-fit, test the hypothesis that the proportion of Americans who do not use the Internet is different from 11%. Use a significance level of 0.05.
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- The National Institute of Mental Health published an article stating that in any two-year period, approximately 10.5percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 150 people in a certain town, eight of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?Suppose that 80% of 3–4-year-old children and 70% of5–8-year-old children in a village are vaccinated with QIVvaccine. Also assume that children who are not vaccinatedhave twice the incidence of influenza as the control groupin Table 3.7.3.29 What % of 3–4-year-old children in the village will getinfluenza?3.30 What % of 5–8-year-old children in the village will getinfluenza?3.31 Suppose we identify a 5–8-year-old child with influenzain the village but are uncertain whether the childwas vaccinated. If we make the same assumptions as inProblems 3.29–3.30, then what is the probability that thechild was vaccinated? (Hint: Use Bayes’ rule here.)An ornithologist thinks that injections of follicle-stimulating hormone (FSH) increase the singing rate of his captive male cotingas (birds). To test this hypothesis, he randomly selects 20 singing cotingas and divides them into two groups of 10 birds each. The first group receives injections of FSH and the second gets injections of saline solution, as a control for the trauma of receiving an injection. He then records the singing rate (in songs per hour) for both groups. The results are given in the following table. Note that two of the FSH birds escaped during injection and were not replaced. a.) What is the alternative hypothesis? Use a directional alternative hypothesis. b.) What is the null hypothesis? c.) Using the Mann-Whitney U test and alpha=0.05tail what is your conclusion?
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- The British Department of Transportation studied to see if people avoid driving on Friday the 13th. They did a traffic count on a Friday and then again on a Friday the 13th at the same two locations. The data for each location on the two different dates is in the table. Do the data show that on average fewer people drive on Friday the 13th? Test at the 5% level.Traffic Count Dates 6th 13th 1990, July 137669 135825 1990, July 129699 128891 1991, September 136898 138275 1991, September 138966 139940 1991, December 132021 129640 1991, December 119268 119214 1992, March 131938 131104 1992, March 123306 124760 1992, November 129499 129219 1992, November 138568 135934A purchaser of transistors buys them in lots of 20. It is his policy to randomly inspect 4components from a lot and to accept the lot if at least 3 are nondefective. Suppose eachlot contains exactly five defective transisters. What proportion of lots are rejected?A graduate student realized that the depression study above in Question 4 should have had a placebo condition in which a third group was given a pill just as the people in the Drug condition were, but where the pill was not Drug D (e.g., a sugar pill). So she designed a new experiment with three conditions -- Drug, No Drug, and Placebo. To perform the experiment, the graduate student randomly assigned 18 people into the three groups so that each group has 6 people. After one month of treatment, all 18 people were asked to rate on a scale from 1 to 7 how depressed they felt, where 1 = not depressed at all and 7 = very depressed. The following are the data: Drug No Drug Placebo 2 4 5 3 5 5 4 5 6 4 4 5 2 6 4 3 6 5 nD = 6 nND = 6 nplacebo = 6 MD = 3 MND = 5 Mplacebo = 5 Using an α-level of .05, perform an…