A sample of n=41n=41 data values randomly collected from a normally distributed population has variance s2=24.2s2=24.2. We wish to test the null hypothesis H0:σ2=17.2H0:σ2=17.2 against the alternative hypothesis H1:σ2>17.2H1:σ2>17.2 at a significance of α=0.05α=0.05. What is the value of the test statistic? Write your answer rounded to 3 decimal places.  What is the critical value? Write your answer rounded to 3 decimal places.

A researcher investigates whether or not a new cold medication affects mental alertness. A standardized test of alertness is normally distributed with μ = 64 and σ = 8.  A random sample of n = 16 students are given the new cold medication and are asked to take the standardized test of alertness. For the sample of n = 16 students, the mean score on the test M = 58. Using the 7 steps of hypothesis testing determine if the new cold medication affects mental alertness (i.e., there is a difference in mental alertness with the cold medication) using α = .05 For this problem 1. State the hypothesis in words   2. State the statistical hypothesis (H1 and Ho)    3. State the α level =   4. State the decision rule and be sure to include the critical value

Independent random samples were selected from two quantitative populations, with sample sizes, means, and variances given below. Population 1 Sample Size 38 45 Sample Mean 9.6 7.3 Sample Variance 10.83 16.49 State the null and alternative hypotheses used to test for a difference in the two population means. О н: (и, - н2) + 0 versus Hа: (и, - и2) %3D 0 О на: (и, - и2) %3D 0 versus H,: (и, — и2) > о О на: (и, - и2) %3D 0 versus Hа: (и, — и2) + 0 О н: (и, — и,) %3D 0 versus H,: (и, — и) о Calculate the necessary test statistic. (Round your answer to two decimal places.) z = 2.77 Calculate the rejection region with a = 0.01. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) z > 2.77 z < 2.77 Draw the appropriate conclusion. O H, is not rejected. There is insufficient evidence to indicate a difference in mean. Ho is not rejected. There is sufficient evidence to indicate a difference in mean. O Ho is rejected. There is insufficient…

Researchers conducted a study to determine whether magnets are effective in treating back pain. The results (higher values indicate larger reductions in pain levels) are shown in the table for the treatment​ (with magnets) group and the sham​ (or placebo) group.                               treatment /sham sample size.      /       19         /    16  mean.             /         10      /      12 standard deviation   /3     /     4 Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Use the critical value method and a 0.01 significance level to test the claim that the treatment mean measure of reduction in back pain is equal to the sham mean measure of reduction in back pain. (Hint: Consider statistictreatment-statisticsham.) Enter the smallest critical value. (Round your answer to nearest thousandth.)

A sample of n=30n=30 data values randomly collected from a normally distributed population has standard deviation s=1.9s=1.9. We wish to test the null hypothesis H0:σ=2.4H0:σ=2.4 against the alternative hypothesis H1:σ≠2.4H1:σ≠2.4 at a significance of α=0.05α=0.05. What is the value of the test statistic? Write your answer rounded to 3 decimal places.  What are the critical values? Write your answers rounded to 3 decimal places.Lower CV:  Upper CV:

A company is doing a hypothesis test on the variation of quality from two suppliers. They believe that one of the suppliers has a different variance than the other supplier and would like to perform a hypothesis test to support their claim. Both distributions are normal, and the populations are independent. use a = 0.01 Ho: σ12- σ2 2 HA:0 1 Supplier 1: standard deviation = 3.54, Sample size = 24 Supplier 2: standard deviation = 8, Sample size = 29. The test statistic (rounded to 4 decimal places) is = The p-value (rounded to 4 decimal places) is = O Reject the null hypothesis - there is enough evidence is support a meaningful difference in the variance of the suppliers. O Fail to reject the null hypothesis - there is not enough evidence to support a meaningful difference in the variance of the suppliers.

You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10.      Ho:μ1=μ2Ho:μ1=μ2      Ha:μ1≠μ2Ha:μ1≠μ2You believe both populations are normally distributed, but you do not know the standard deviations for either. We will assume that the population variances are not equal. You obtain a sample of size n1=17 with a mean of M1=64.6 and a standard deviation of SD1=11.7 from the first population. You obtain a sample of size n2=17 with a mean of M2=53.2 and a standard deviation of SD2=8.9 from the second population.What is the test statistic for this sample? (Report answer accurate to three decimal places.)

Suppose 26 of 200 tires of brand A failed to last 30000 miles, whereas the corresponding figure for 200 tires of brands B was 32. Test the null hypothesis that there is no difference in the quality of the two kinds of tires at the α=:05 significance level.

A sample of n=40n=40 data values randomly collected from a normally distributed population has variance s2=11.7s2=11.7. We wish to test the null hypothesis H0:σ2=7.1H0:σ2=7.1 against the alternative hypothesis H1:σ2≠7.1H1:σ2≠7.1 at a significance of α=0.01α=0.01. What is the value of the test statistic? Write your answer rounded to 3 decimal places. What are the critical values? Write your answers rounded to 3 decimal places. Lower CV:  Upper CV:

Construct a 95% confidence interval for μ1 - μ2. Two samples are randomly selected from normal populations. The sample statistics are given below. Assume that σ21 = σ22.n1 = 8 n2 = 7x1 = 4.1 x2 = 5.5s1 = 0.76 s2 = 2.51