Consider the hypothesis test Ho :µ1 = µz against H1 : µ1 # µ2 with known standard deviations o = 9 and o2 = 5. Suppose that sample sizes nį = 11 and n2 = 14 and that I = 4.5 and I2 = 8.0. Use a = 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) for a true difference in means of 3? (c) Assuming equal sample sizes, what sample size should be used to obtain ß = 0.05 if the true difference in means is 3? Assume that a = 0.05. (a) The null hypothesis rejected. The P-value is i .Round your answer to three decimal places (e.g. 98.765).

To compare the dry braking distances from 30 to 0 miles per hour for two makes of​ automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10​, can the engineer support the claim that the mean braking distances are different for the two makes of​ automobiles? Assume the samples are random and​ independent, and the populations are normally distributed.   The critical​ value(s) is/are   Find the standardized test statistic z for μ1−μ2.

If the researcher decides to test this hypothesis at the = 0.05 level of significance, determine the critical value. The critical value are=_ and=_. Round to three decimal places as needed.

We collected a sample of twenty-five observations. We assumed that the observations are from a population whose values follow a normal distribution with a mean of u and a standard deviation of five. We performed a test with these hypotheses Ho: μ = 0H₁ = 0 and H₁ : μ0H₁0. The test statistic is the sample mean . The 5% rejection region is 1.959964 > 1.959964. What is the power of this test when μ = -2μ = -2? Please state the statistical power up to the fourth decimal place.

Suppose the mean IQ score of people in a certain country is 100. Suppose the director of a college obtains a simple random sample of 39 students from that country and finds the mean IQ is 104.5 with a standard deviation of 13.6. Complete parts (a) through (d) below. (a) Consider the hypotheses Ho: µ= 100 versus H,: µ> 100. Explain what the director is testing. Perform the test at the a = 0.10 level of significance. Write a conclusion for the test. Explain what the director is testing. Choose the correct answer below. O A. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not equal to 100. OB. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually greater than 100. O C. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not greater than 100. O D. The director is testing if the sample provided sufficient…

Scores on an IQ test are normally distributed.  A sample of 25 IQ scores had variance of 64.  The developer of the test claims that the population standard deviation is 15.  Do these data provide sufficient evidence to significance?  Use α=0.05α=0.05 .  Answer the following questions. (a) What is the parameter?   . (input as  "mean", "standard deviation", "variance" or "proportion") (b) Determine if the alternative hypothesis is "right", "left" or "two-tailed" test.    (input as "right", "left" or "two-tailed") (c) Test by using a confidence interval.   Round confidence interval to nearest thousandth.  (e.g.  0.1345 would be entered as 0.135) between (  and  ) (d) State conclusion.:  There is  (input as "sufficient" or "insufficient") to  (input as "conclude" or "reject")  to conclude that the population standard deviation of IQ test is 15.

You wish to test Ho: μ₁ μ2 versus Ha:μ₁ μ₂ at a = = 0.10. You obtain a sample of size n₁ 1 = 58.2 and a standard deviation of $₁ = 20.9 from the first population. You obtain a sample 40.2 and a standard deviation of $2 = 5.6 from the second 9 with a mean of 2 a mean of of size n2 population. = = What is the test statistic? = = 6 with Assume that the data come from normal populations with equal variances. Round your answers to three decimal places, and round any interim calculations to four decimal places.

A researcher wishes to see if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. She selects two random samples and the data are shown. Use μ1 for the mean number of families with no children. At α=0.10, is there a difference between the means? Use the P-value method and tables. (a) State the hypothesis and identify the claim with the correct hypothesis. H0:  ▼(Choose one) H1:  ▼(Choose one) This hypothesis test is a ▼(Choose one) test.       (b)Find the critical value(s). Round the answer to 3decimal places, if necessary. If there ismore than one critical value,   Critical values:   (c)Compute the test value. Round the answer to at least 3 decimal places, if necessary. z= Compute the P -value. Round the answer to four decimal places. P-value=   (d)Make the decision. What's the null hypothesis? (e)Summarize the…

= You wish to test Ho: d 0 versus Ha: Md > 0 at a significance level of 0.10. For the context of this problem, d = μ2 μ₁ where the first data set represents a pre-test and the second data set represents a post-test. You obtain pre-test and post-test samples for nd 18 subjects. The average difference -= (post-pre) is d 3.8 with a standard deviation of the differences of sa 32.6. Round your answers to three decimal places, and round any interim calculations to four decimal places. What is the test statistic? - - -

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with o = 6. The hypotheses H,: µ = 74 and H: µ < 74 are to be tested using a random sample of n = 25 observations. (a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.) 1.42 standard deviations (b) If x = 72.3, what is the conclusion using a = 0.004? Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = p-value = State the conclusion in the problem context. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74. O Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74. O Reject the null…