(1 point) A random sample of 100 observations from a population with standard deviation 7.22257393008022 yielded a sample mean of 91.2.(a) Given that the null hypothesis is u = 90 and the alternative hypothesis isu > 90 using a = .05, find the following:(i) critical z score(ii) test statistic =(b) Given that the null hypothesis is u = 90 and the alternative hypothesis is u + 90 using a = .05, find the following:(1) the positive critical z score(ii) the negative critical z score(iii) test statistic =

a) Given : Given data : sample size, n = 100 sample mean, x̄ = 91.2 population…

Answered: (a) Given that the null hypothesis is u…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Use the given information to find the P-value. Also, use a 0.05 significance level and state theconclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis).With H1: p (does not equal) 3/5, the test statistic is z = 0.78
A nutritionist wants to investigate whether her new diet will be effective in helping women aged 30-40 to lose weight. She will use a paired sample to determine whether the mean weight of women before going on this diet is greater than the mean weight of women after being on this diet for two months. Determine the null and alternative hypotheses for the proposed hypothesis test. O A. Let μ₁ denote the mean weight of women before going on this diet and let μ₂ denote the mean weight of women who have been on this diet for two months. The null and alternative hypotheses are Ho: H₁ H2 and Ha: H₁ H₂. O D. Let μ₁ denote the mean weight of women before going on this diet and let μ₂ denote the mean weight of women who have been on this diet for two months. The null and alternative hypotheses are Ho: H₁ H2 and Ha: H₁ H₂.
On its municipal website, the city of Tulsa states that the rate it charges per 5 CCF of residential water is $21.62. How do the residential water rates of other U.S. public utilities compare to Tulsa's rate? The data shown below ($) contains the rate per 5 CCF of residential water for 42 randomly selected U.S. cities. 10.48 9.18 11.8 6.5 12.42 14.53 15.56 10.12 14.5 16.18 17.6 19.18 17.98 12.85 16.8 17.35 15.64 14.8 18.91 17.99 14.9 18.42 16.05 26.85 22.32 22.76 20.98 23.45 19.05 23.7 19.26 23.75 27.8 27.05 27.14 26.99 24.68 37.86 26.51 39.01 29.46 41.65 (a) Formulate hypotheses that can be used to determine whether the population mean rate per 5 CCF of residential water charged by U.S. public utilities differs from the $21.62 rate charged by Tulsa. (Enter != for # as needed.) Ho: (b) What is the test statistic for your hypothesis test in part (a)? (Round your answer to three decimal places.) What is the p-value for your hypothesis test in part (a)? (Round your answer to four decimal…
(a) State the alternative hypothesis.(b) State the type of the test required and its rejection area at 0.05 significance level.(c) Calculate the test statistic, Z for the population proportion.
Women athletes at a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 23 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 10% level of significance. What is the level of significance? (b) State the null and alternate hypotheses. H0: p = 0.67; H1: p > 0.67 H0: p = 0.67; H1: p ≠ 0.67 H0: p < 0.67; H1: p = 0.67 H0: p = 0.67; H1: p < 0.67 What sampling distribution will you use? The Student's t, since np < 5 and nq < 5. The standard normal, since np < 5 and nq < 5. The standard normal, since np > 5 and nq > 5. The Student's t, since np > 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) Find the P-value of the test statistic. (Round your answer to four decimal places.)…
A large cookie company claims the average amount of sodium per cookie is 200 mg. You suspect that the sodium content is different than that, so you take a random sample of 36 cookies and research the nutritional content. You then conduct a hypothesis test that u = 200 vs. the alternative that u + 200. (a) The standardized test statistic for your sample is 2.7. The P-value would then be: A) 0.9965 B) 0.4983 C) 0.0070 D) 0.0035 Selection: (b) Which would be the correct decision for your hypothesis test? A) Reject Ho B) Do not reject Ho Selection: (C) A Type I Error in this situation would be: A) Concluding that p 200 when in fact u = 200 is true. B) Concluding that u = 200 when in fact p 200 is true. C) Concluding that u = 200 when in fact p = 200 is true. D) Concluding that u 200 when in fact u 200 is true. %3D
A large cookie company claims the average amount of sodium per cookie is 200 mg. You suspect that the sodium content is different than that, so you take a random sample of 36 cookies and research the nutritional content. You then conduct a hypothesis test that μ = 200 vs. the alternative that μ ≠ 200. (a) The standardized test statistic for your sample is 2.7. The P-value would then be: A) 0.9965 B) 0.4983 C) 0.0070 D) 0.0035 Selection: (b) Which would be the correct decision for your hypothesis test? A) Reject H0 B) Do not reject H0 Selection: (c) A Type I Error in this situation would be: A) Concluding that μ ≠ 200 when in fact μ = 200 is true. B) Concluding that μ = 200 when in fact μ ≠ 200 is true. C) Concluding that μ = 200 when in fact μ = 200 is true. D) Concluding that μ ≠ 200 when in fact μ ≠ 200 is true. Selection:
According to a leasing firm's reports, the mean number of miles driven annually in its leased cars is 13,600 miles with a standard deviation of 2820 miles. The company recently starting using new contracts which require customers to have the cars serviced at their own expense. The company's owner believes the mean number of miles driven annually under the new contracts, u, is less than 13,600 miles. He takes a random sample of 50 cars under the new contracts. The cars in the sample had a mean of 13,499 annual miles driven. Is there support for the claim, at the 0.10 level of significance, that the population mean number of miles driven annually by cars under the new contracts, is less than 13,600 miles? Assume that the population standard deviation of miles driven annually was not affected by the change to the contracts. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified…
A personnel director in a particular state claims that the mean annual income is greater in one of the state's counties (county A) than it is in another county (county B). In County A, a random sample of 6 residents has a mean annual income of $41,400 and a standard deviation of $8400. In County B, a random sample of 8 residents has a mean annual income of $39,800 and a standard deviation of $5200. At a = 0.10, answer parts (a) through (e). Assume the population variances are not equal. If convenient, use technology to solve the problem. (a) Identify the claim and state Ho and Ha. Which is the correct claim below? A. "The mean annual income in county A is less than in county B." B. "The mean annual incomes in counties A and B are not equal." C. "The mean annual incomes in counties A and B are equal." D. "The mean annual income in county A is greater than in county B." What are H, and Ha? The null hypothesis, Ho, is The alternative hypothesis, Ha, is Which hypothesis is the claim? The…
(a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean appreciation rate of houses in Sun Beach, μ1 , is higher than μ2 , the mean appreciation rate of houses in North Arden? Yes No
The null hypothesis is H0: μ1=μ2 and the alternative hypothesis is Ha: μ1≠μ2. The data in the accompanying table are from a simple random paired sample from the two populations under consideration. Use the paired t-test to perform the required hypothesis test at the 10% significance level. Pair Population 1 Population 2 1 9 7 2 10 9 3 14 10 4 13 6 5 8 5 6 15 16 7 18 15 Find the test statistic. Use population 1 population 2 as the difference.t = ___________________ (Round to two decimal places as needed.)
a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) and (e) Can we conclude that the mean travel time via the 10 freeway, μ1 , is different from μ2 , the mean travel time via the 60 freeway? Yes No

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