Researchers equipped random samples of 46 male and 58 female students from a large university with a small device that secretly records sound for a random 30 seconds during each 12.5-minute period over two days. Then they counted the number of words spoken by each subject during each recording period and, from this, estimated how many words per day each subject speaks. The female estimates had a mean of 16,177 words per day with a standard deviation of 7520 words per day. For the male estimates, the mean was 16,569 and the standard deviation was 9108. Do these data provide convincing evidence of a difference in the average number of words spoken in a day by male and female students at this university? What is the test statistic for this test? What is the p-value for this test? What is the critical value for this test? What is the decision for this test?

Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average (mean) of 32 grams of fat per pound, with a standard deviation of 8 grams of fat per pound. A random sample of 40 farm-raised trout is selected. The mean fat content for the sample is 30.2 grams per pound. Find the probability of observing a sample mean of 30.2 grams of fat per pound or less in a random sample of 40 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places. Check esc 23 2$ 5 2 e r t y tab

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According to the historical data, the life expectancy in the United States is less than or equal to the life expectancy in Ireland. A new study has been made to see whether this has changed. Records of 235 individuals from the United States who died recently are selected at random. The 235 individuals lived an average of 77.6 years with a standard deviation of 6.7 years. Records of 220 individuals from Ireland who died recently are selected at random and independently. The 220 individuals lived an average of 76.3 years with a standard deviation of 5.5 years. Assume that the population standard deviations of the life expectancies can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.1 level of significance, is there enough evidence to support the claim that the life expectancy, u,, in the United States is greater than the life expectancy, µ, in Ireland? Perform a one-tailed test. Then fill in the table below. Carry…

Researchers want to compare the relative effectiveness of two popular diets. They randomly assign each of 400 volunteers to one of two Groups: A & B.  There are 200 volunteers in each group. Group A spends 6 months on Diet A. Group B spends 6 months on Diet B.   At the beginning of the study, the difference in average weight between the two groups was negligible. After the study, the Group A had lost on average 7.8 pounds with a standard deviation of 13.4 pounds, while the Group B had lost on average 5.3 pounds with a standard deviation of 14.8 pounds. Determine the z-score/test statistic for a two-tailed test with significance level α = 0.05 , accurate to 2 decimal places.

A random sample of 34 chemists from Washington state shows an average salary of $41857, the population standard deviation for chemist salaries in Washington state is $697. A random sample of 35 chemists from Florida state shows an average salary of $44632, the population standard deviation for chemist salaries in Florida state is $900. A chemist that has worked in both states believes that chemists in Washington make a different amount than chemists in Florida. At a=0.05 is this chemist correct? Let Washington be sample 1 and Florida be sample 2. The correct hypotheses are: Ο Ηο: μι μ2(claim) Ο Ηο: μι 2 με HAM12(claim) Ho: M₁ = H2 1 HAM12(claim) Since the level of significance is 0.05 the critical value is 1.96 and -1.96 The test statistic is: (round to 3 places) The p-value is: (round to 3 places)

In a 430-page manuscript, there are 270 randomly distributed misprints. Use the Poison approximation. Find the mean number 2 of misprints per page. Round to one decimal place as needed.

A dentist wants to estimate the average number of patients coming into her clinic each day. She estimates the standard deviation is 6 patients per day. If she wants to use a random sample of previous days for her sample, how many days should she include to be 95% sure her estimate is off by no more than 0.3 patients per day?