The critical value for a two-tailed hypothesis test with a level of significance of α = 0.05 when a standardized test statistic has a standard normal distribution is z* =
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The critical value for a two-tailed hypothesis test with a level of significance of α = 0.05 when a standardized test statistic has a standard
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- A researcher measures human calcitonin (HCT) levels in men with rheumatoid arthritis. The researcher randomly selects 26 men with rheumatoid arthritis and measures the samplemean HCT level of 33.8 pg/mL and a sample standard deviation of 10.4 pg/mL. Assume thatHCT for individuals with rheumatoid arthritis follows a normal distribution. Construct a 92%confidence interval for the mean HCT level in men with rheumatoid arthritis. Be sure to: State the value for α. State whether you should use z or t and find the appropriate value. State the parameter your confidence interval is for. Find the confidence interval (to 2 decimals). Write a verbal interpretation of your confidence interval. (For example: We are xx%confident...)Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was 4.5 days, and the standard deviation of overall duration of symptoms was 1.6 days. For the placebo group, the mean overall duration of symptoms was 8 days, and the standard deviation was 1.8 days. (a) Calculate a 95% confidence interval for the mean overall duration of symptoms in a population of individuals like those who used the zinc lozenges. (Round your answers to two decimal places.)to days(b) Calculate a 95% confidence interval for the mean overall duration of symptoms in a population of individuals like those who used the placebo lozenges. (Round your answers to two decimal places.)to days(c) On the basis of the intervals computed in parts (a) and…What is the critical value of a one-tailed greater than One-Sample Z-Test for Mean where alpha equals 0.05?
- An incubation period is a time between when you contract a virus and when your symptoms start. Assume that the population of incubation periods for a novel coronavirus has an unknown population standard deviation. By surveying randomly selected local hospitals, a researcher was able to obtain a sample of incubation periods of 40 patients with the average of the data of 9 days and the standard deviation of 3 days. At 10% significance level, test the claim that the average incubation period of the novel coronavirus is different from 7 days.A company that produces top-of-the-line batteries claims that its batteries are good, on average, for more than 65 months. A consumer protection agency tested 25 such batteries to check this claim. It found that the mean life of these 25 batteries is 63.4 months, and the standard deviation is 3 months. If we test the company’s claim at a 5% significance level, what is the p-value? Assume normality. A company that produces top-of-the-line batteries claims that its batteries are good, on average, for more than 65 months. A consumer protection agency tested 25 such batteries to check this claim. It found that the mean life of these 25 batteries is 63.4 months, and the standard deviation is 3 months. If we test the company’s claim at a 5% significance level, what is the p-value? Assume normality. 0.0067 0.0135 0.9962 0.9933Bone mineral density (BMD) is a measure of bone strength. Studies show that BMD declines after age 45. The impact of exercise may increase BMD. A random sample of 59 women between the ages of 41 and 45 with no major health problems were studied. The women were classified into one of two groups based upon their level of exercise activity: walking women and sedentary women. The 39 women who walked regularly had a mean BMD of 5.96 with a standard deviation of 1.22. The 20 women who are sedentary had a mean BMD of 4.41 with a standard deviation of 1.02. Which of the following inference procedures could be used to estimate the difference in the mean BMD for these two types of women
- The amount of water consumed each week by Bronx residences is normally distributed. The population mean of water consumption is 120.3 gallons with a standard deviation of 10.0 gallons. Test the claim at the 0.10 significance level that the average amount of water consumed is not 125 gallons with a sample size of 100 residences. Do you retain or reject the null hypothesis?A leasing firm claims that the mean number of miles driven annually, µ, in its leased cans is less than 12460 miles. A random sample of 27 cars leased from this firm had a mean of 11839 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 1620 miles. Assume that the population is normally distributed. Is there support for the firm’s claim at the 0.05 level of significance? The null hypothesis: H0 : _____ The alternative hypothesis: H1: ______ The type of test statistic: (choose one) _______ The value of the test statistic: ______ (round to at least three decimal places.) The p-value: _____ (round to at least three decimal places.) Can we support the leasing firm’s claim that the mean number of miles driven annually is less than 12460 miles? Yes _____, NO ______For an upper-tail test at the 1% significance level, what is the appropriate critical value when a sample of size 28 is drawn from a normal population with unknown standard deviation?
- A businessman is considering investing in a small business. A random sample of 45companies revealed that the mean was 9.6% of return and the standard deviation was1.2%. Do the data support that the return is less than 10% with significance levelα=0.02; 0.04; 0.05; 0.06; 0.08? Use P-value.Among private universities in the United States, the mean ratio of students to professors is 35.2 (i.e., 35.2 students for each professor) with a standard deviation of 8.8. Suppose a random sample of 50 universities is selected and the observed mean student-to-professor ratio is 38. Is there evidence that the reported mean ratio actually exceeds 35.2? Use alpha = 0.05 and conduct the appropriate hypothesis test. What is the critical value of the test?a. z = 1.645b. z= 2.25c. z=1.96d. t = 1.677A scientist wants to know if the average weight of a particular species of fish is different from 500 grams. He collects a sample of 15 fish and finds that their average weight is 490 grams with a standard deviation of 20 grams. Can he reject the null hypothesis that the true average weight of the fish is 500 grams, using a one sample t-test with a significance level of 0.05?
