The width of the confidence interval estimate of the population mean μ is a function of only two quantities: the population standard deviation σ and the sample size n
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The width of the confidence
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- A hypothesis test comparing two population variances uses the F distribution. The F distribution is not symmetric and its shape will depend on two values of degrees of freedom, a numerator and denominator degrees of freedom. It is important to note that the F values will never be negative. The F test statistic is calculated as follows where s12 is the variance from sample 1, s22 is the variance from sample 2, and s12 > s22. Since the F statistic is calculated using the larger variance as the numerator, only upper tail areas will be used when finding the p-value. F = s12 s22 The size of sample 1 is denoted by n1 and will have n1 − 1 degrees of freedom. The size of sample 2 is denoted by n2 and will have n2 − 1 degrees of freedom. It is given that a sample of 21 items from population 1 has a variance of s12 = 5.5. A sample of 26 items from population 2 has a variance of s22 = 2.25. Use these values to find the F test statistic, rounding the result to two decimal places.…Assume that both populations are normally distributed. (a) Test whether u, #H2 at the a= 0.05 level of significance for the given sample data. (b) Construct a 95% confidence interval about u, - Ha. Population 1 Population 2 15 15 8.7 3.2 11.4 3 ... (a) Test whether u, # 2 at the a = 0.05 level of significance for the given sample data. Determine the null and alternative hypothesis for this test. O A. Ho H, # 42 O B. Ho H1 = H2 OC. Ho H1 = H2 O D. Ho H, #H2 Question ViewerUse the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance a, and sample sizes n, and n2. Assume that the samples are independent, normal, and random. Answer parts (a) and (b). Ha H >H2; a = 0.05, n, = 14, n = 13 (a) Find the critical value(s) assuming that the population variances are equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)
- Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed. c=0.90 x overbarx=13.2 s=4.0 n=7A sample mean, sample standard deviation, and sample size are given. Use the one-mean t-test to perform the required hypothesis test about the mean, μ, of the population from which the sample was drawn. Use the critical-value approach. Sample mean = 3.12 s = 0.59 n = 9 α = 0.01 H0: µ = 2.85 H1: µ > 2.85 The critical value(s) is/are (If there are two critical values separate each with a comma and list from smallest to largest.)Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance a, and sample sizes n, and n2. Assume that the samples are independent, normal, and random. Answer parts (a) and (b). %3D Ha: 12, a=0.02, n, = 15, n2 =8 (a) Find the critical value(s) assuming that the population variances are equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) (b) Find the critical value(s) assuming that the population variances are not equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) Next 2:15 PM 66°F Mostly cloudy ^ ED a 0 P Type here to search 11/22/2021 Inser 四 F6 PrtSc F3 F4 F5 F7 F8 F9 F10 F11 F12 F2 23 %24 & 3. 4 6. 7. 8 + II 团 5
- Use the t-distribution to find a confidence interval for a mean u given the relevant sample results. Give the best point estimate for μ, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 90% confidence interval for using the sample results Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places. point estimate = i margin of error = The 90% confidence interval is i = 142.5, s = to i 55.7, and n = 50Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed. c=0.99, x=13.4, s=3.0, n=5 (_,_) ?Construct the indicated confidence interval for the population mean mu using the t-distribution. Assume the population is normally distributed. c=0.90, x overbar=13.1, s=0.64, n=19
- Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give the best point estimate for μ, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed.A 90% confidence interval for μ using the sample results x¯=138.9, s=57.0, and n=50Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places.point estimate = margin of error = The 90% confidence interval isTest the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. A manufacturer uses a new production method to produce steel rods. A random sample of 37 steel rods resulted in lengths with a mean a+1 and standard deviation of 4.7 cm. At the 0.10 significance level, test the claim that the new production method has mean 5.5 cm, which was the mean for the old method. a=2A sample mean, sample standard deviation, and sample size are given. Use the one-mean t-test to perform the required hypothesis test about the mean, μ, of the population from which the sample was drawn. Use the critical-value approach. Sample mean = 7.1 s = 2.3 n = 18 α = 0.01 H0: µ = 10 H1: µ < 10 The critical value(s) is/are (If there are two critical values separate each with a comma and list from smallest to largest)
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