A manufacturer claims him market share is 60%. However a random sample of 500 clients show that only 275 supports his product. Test the manufacturer’s statement at 1% significance level.
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A manufacturer claims him market share is 60%.
However a random sample of 500 clients show that only 275
supports his product. Test the manufacturer’s statement at 1%
significance level.
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- A researcher at a college hears students complain that they don’t have enough time to in their week to study. He believes that the students at the college are spending much more time on Facebook, Twitter, and Instagram than they did three years ago. He knows that three years ago, the mean number of hours per week students spent of social media was 15.1 hours. He takes a sample of 16 students and finds they spend 23.3 hours per week on social media with SS=240.Measure effect size using percentage of varianceThe athletic director at a large university compared the proportions of freshmen (1st year students) and seniors (4th year students) who exercise regularly. She analyzed the data and found the Z-statistic for the difference between the population proportions to be 2.43 with a P-value of 0.015. The level of significance was set at 0.05. State the conclusion she can draw about the difference between the two population proportions.A recent study indicated that 18% of people free from cardiovascular disease were considered obese. An investigator hypothesizes that a higher proportion of patients with a history of cardiovascular disease will be considered obese. Including 464 patients in the study would ensure that the power of the test is 80% to detect a 5% difference in the proportion with obesity. True or False?
- A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.0 ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. Believing that the mean amount of coffee dispensed by the machine, u, is greater than 7.0 ounces, BIG plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 7.4 ounces and that the standard deviation is 0.3 ounces. Based on this information, answer the questions below. What are the null hypothesis (H) and the alternative hypothesis (H,) that should be used for the test? H: u is ? Η: μs7 In the context of this test, what is a Type I error? v the hypothesis that u is ? ? v. A Type I error is ? v|? when, in fact, u is ? Suppose that BIG decides to reject the null hypothesis. What sort of error might it be making? ?A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.3 ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. Believing that the mean amount of coffee dispensed by the machine, u, is greater than 7.3 ounces, BIG plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 7.5 ounces and that the standard deviation is 0.6 ounces. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? H: u is ? H: u is ? In the context of this test, what is a Type I error? A Type I error is ? fact, u is ? v the hypothesis that u is ? v? v. when, in Suppose that BIG decides not to reject the null hypothesis. What sort of error might it be making? ?An important measure in the study of contagious infectious diseases is the number of cases directly generated by one previous case. Jessica is an epidemiologist studying the spread of an infectious disease in her country. She claimed that the mean number of cases directly generated by one previous case is now greater than 1.2. A study of 12 randomly selected cases of the disease is conducted and finds the sample mean number of cases directly generated by one previous case to be 1.5 with a sample standard deviation of 0.7. Assume that the population of the number of cases directly generated by one previous case is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to support the claim that u, the mean number of cases directly generated by one previous case, is greater than 1.2. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test.…
- A dietician read in a survey that 70.5% of adults in the U.S. do not eat breakfast at least 3 days a week. She believes that the proportion that skip breakfast 3 days a week is different than 0.705. To verify her claim, she selects a random sample of 71 adults and asks them how many days a week they skip breakfast.. 44 of them report that they skip breakfast at least 3 days a week. Test her claim at a = 0.10. The correct hypotheses would be: О Но:р 0.705 (claim) Но: р > 0.705 HA:p < 0.705 (claim) О Но: р — 0.705 HA:P + 0.705 (claim) Since the level of significance is 0.10 the critical value is 1.645 and -1.645 The test statistic is: (round to 3 places) The p-value is: (round to 3 places) The decision can be made to: O reject Ho O do not reject Ho The final conclusion is that: O There is enough evidence to reject the claim that the proportion that skip breakfast 3 days a week is different than 0.705. O There is not enough evidence to reject the claim that the proportion that skip…During the 1990s, the fatality rate for lung cancer was 80 per 100,000 people. After the turn of the century and the establishment of newer treatments and adjustment in public health advertising, a random sample of 10,000 people exhibits only six deaths due to lung cancer. Test at the 0.05 significance level whether that data are proof of a reduced fatality rate for lung cancer. b. Make the decision rule. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) c. Evaluate the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. Some governments have a safety limit for cadmium in dry vegetables at 0.56 part per million (ppm). A research team measured the cadmium levels in a random sample of edible mushrooms, where the hypothesis test is to decide whether the mean cadmium level in the sample is greater than the governments' safety limit. The null and alternative hypotheses are H0: μ=0.56 ppm, Ha: μ>0.56 ppm. Complete parts (a) through (e) below. d. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean cadmium level in that type of mushrooms equals the safety limit of 0.56 ppm. Choose the correct answer below. A. type I error B. correct decision because a true null hypothesis is not rejected C. correct decision because…
- This research was conducted with Korean adolescents in the Los Angeles area. Would you be willing to generalize the results of this study to Korean adolescents who live in other regions of the country? Why or why not.According to Security Magazine, 83% of ransomware victims paid to restore access to their data. Assume that a random sample of 200 ransomware victims in UAE showed that 79% paid to restore their data. We are interetsed in testing whether the percentage of ransomware victims who paid to restore their data in UAE is lower than the global rate. The p-value of the test isCitrus Rental is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage over the years for Citrus cars has been about 1500 miles per month. Recently, though, Citrus purchased thousands of new cars, and the company claims that the average mileage of its cars is now less than in the past. To test this, a random sample of 11 recent mileages of Citrus cars was taken. The mean of these 11 mileages was 1332 miles per month, and the standard deviation was 232 miles per month. Assume that the population of recent monthly mileages of Citrus cars is normally distributed. At the 0.05 level of significance, can it be concluded that the mean recent monthly mileage, u, of Citrus cars is less than 1500 miles per month? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary,…