BIG Corporation advertises that its light bulbs have a mean lifetime, u, of 3200 hours. Suppose we have good reason to believe that u is different from 3200 hours and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 3400 hours and that the sample standard deviation of the lifetimes is 600 hours. Based on this information, complete the parts below. (a) What are the null hypothesis Ho and the alternative hypothesis H, that should be used for the test? H. : 3200 OSO H, : 3200 (b) Suppose that we decide to reject the null hypothesis. What sort of error might we be making? Type II (c) Suppose the true mean lifetime of BIG's light bulbs is 3420 hours. Fill in the blanks to describe a Type II error. A Type II error would be (Choose one) v the hypothesis that u is (Choose one) (Choose one) ▼ when, in fact, u is (Choose one)

In the year 2033, katy perry is a leading traveling nurse. Katy is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Katy takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. g) What is the interpretation (not your conclusions) of the p value in the context of the problem you found in part e? h) What are your conclusions in the context of the problem? Relate your conclusions to the test statistic and critical value, confidence interval and p value.

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In a certain country the heights of adult men are normally distributed with a mean of 69.7 inches and a standard deviation of 2.5 inches. The country's military requires that men have heights between 65 inches and 76 inches. Determine what percentage of this country's men are eligible for the military based on height. The percentage of men that are eligible for the military based on height is (Round to two decimal places as needed.) %. (1) U +

Last year, the standard deviation of the ages at UTM was 1.8 years. Recently, a sample of 61 students had a standard deviation of 2.1 years. We are interested in testing to see if there has been a significant increase in the standard deviation of the ages of the students at UTM. Assume ages are Normally distributed. The p-value for this test is

In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 3030 scores from all of the students who took the test. She sees that the mean score is 169169 with a standard deviation of 7.06747.0674. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 1313. Is there evidence that the standard deviation of test scores has decreased at the α=0.005α=0.005 level? Assume the population is normally distributed. Step 1 of 5:  State the null and alternative hypotheses. Round to four decimal places when necessary. Step 2 of 5:  Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.     Step 3 of 5:  Determine the value of the test statistic. Round your answer to three decimal places. Step 4 of 5:  Make the…

Some college graduates employed full-time work more than 40 hours per week, and some work fewer than 40 hours per week. We suspect that the mean number of hours worked per week by college graduates, u, is less than 40 hours and wish to do a statistical test. We select a random sample of college graduates employed full-time and find that the mean of the sample is 35 hours and that the standard deviation is 3 hours. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? H: u is ? H: u is ? In the context of this test, what is a Type II error? A Type II error is ? fact, u is ? v the hypothesis that u is ? ? v. when, in Suppose that we decide to reject the null hypothesis. What sort of error might we be making? ?

The mean age of all 663 used cars for sale in a newspaper one Saturday last month was 7.5 years, with a standard deviation of7.1 years. The distribution ads, a reporter randomly selects 50 of these used cars and plans to visit each owner to inspect the cars. He finds that the mean age of the 50 cars he sam Complete parts a through c. a From the problem statement, which of the values 75,7.1, 7.9, and 5.6 are parameters and which are statistics? The value 7.5 is a The value 7.1 is a The value 7.9 is a The value 5.6 is a

During the busy season, it is important for the shipping manager at ShipMundo to be able to estimate the time it takes the loading crew to load a truck. The shipping manager has found that she can model the load times using a normal distribution with a mean of 152 minutes and a standard deviation of 15 minutes. Use this table or the ALEKS calculator to find the percentage of load times between 116 minutes and 149 minutes according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).

a sample of n=16 scores is selected from a population with a mean of 60 and a standard deviation of 24. If the sample mean is M=66, what is the z-score for this sample mean?