The historical reports from two major networks showed that the mean number of commercials aired during prime time was equal for both networks last year. In order to find out whether they still air the same number of commercials on average or not, random and independent samples of 65 recent prime time airings from both networks have been considered. The first network aired a mean of 109.2 commercials during prime time with a standard deviation of 5.1. The second network aired a mean of 110.8 commercials during prime time with a standard deviation of 5.4. Since the sample sizes are quite large, assume that the population standard deviations can be estimated to be equal to the sample standard deviations, 5.1 and 5.4. At the 0.05 level of significance, is there sufficient evidence to support the claim that the mean number, μ₁, of commercials aired during prime time by the first station is not equal to the mean number, μ₂, of commercials aired during prime time by the second station? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho :O H₁ :0 (b) Determine the type of test statistic to use. Z (c) Find the value of the test statistic. (Round to three or more decimal places.) lir three or more decimal places.) 3 1x X 5 O X S 2 =O OSO 口<口 P S <2 010 ロマロ >

According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 64 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively. (a) Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (Enter != for # as needed.) Ho: H: (b) Using the sample from the 64 bottles, what is the test statistic? (Round your answer to three decimal places.) Using the sample from the 64 bottles, what is the p-value? (Round your answer to four decimal places.) p-value =…

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. They are also interested in the variation of the number of Babies. Suppose that an airline executive believes the standard deviation in the number of babies is 6 at the most. The airline conducts a survey. The results of the 23 flights surveyed give a samle mean of 8 with a sample standard deviation of 9. Test the executive's belief to see if it is accurate, or if it is actually greater at the a = 0.05 level. Ho:o = H:o Select an answer df = P-value = The p-value is... greater than a less than (or equal to) a This test statistic leads to a decision to... reject the null fail to reject the null accept the alternative accept the null As such, the final conclusion is that there Select an answer v sufficient evidence to conclude the standard deviation of the number of babies on airplanes is Select an answer than (?

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.

The mean work week for engineers in start-up companies is claimed to be about 59 hours with a standard deviation of 6 hours. Kara, a newly hired engineer hopes that it's not (she wants it to be shorter). She asks 10 engineers in start-ups for the lengths of their mean work weeks. Their responses are 70; 45; 55; 60; 65; 55; 55; 60; 50; 55.a. Is the newly hired engineer testing a mean or a proportion? mean proportion Correct b. The null hypothesis (or company claim), in symbols, is μ=μ=Correct.c. If the claim is correct, what is the probability that a sample mean would be as low as Kara's mean?Incorrect %Give your answer as a percentage accurate to one decimal place.

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In a sample of 351 gamers between the ages of 16-25, the mean number of hours spent gaming per week was 42.5 hours. In a sample of 269 gamers between the ages of 26-40, the mean number of hours spent gaming per week was 43.8 hours. If the population standard deviation for the mean number of hours spent gaming per week is 9.5 for the age group 16-25 and 10.7 for the age group 26-40, test the claim that gamers between the ages of 16-25 spend less time gaming per week than gamers between the ages of 26-40. Assume α=0.03.      Let population 1 be gamers in the age group 16-25 and population 2 be gamers in the age group 26-40. Round the test statistic to two decimal places, and round the p-value to four decimal places.   The test statistic is . The p-value is . Should the null hypothesis be rejected?

An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 240 Fundash runners and 200 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 240 Fundash runners complete the course with a mean time of 76.7 minutes and a standard deviation of 5.2 minutes. The 200 Coolsprint runners complete the course with a mean time of 77.5 minutes and a standard deviation of 5.4 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, μ1 , of Fundash is not equal to the mean completion time, μ2 , of Coolsprint?…

A college in the northeastern United States used SAT scores to help decide which applicants to admit. To determine whether the SAT was useful in predicting success, the college examined the relationship between the SAT scores and first-year GPAs of admitted students. The average math SAT score of a sample of 200 randomly selected students was 649.5 with a standard deviation of 66.2. The average GPA of the same students was 2.63 with a standard deviation of 0.58. The correlation between GPA and math SAT score was 0.19. (a) What does the correlation of 0.19 tell us about SAT scores and GPA scores? (You need to provide two answers.)(b) Find the equation of the least squares regression line.(c) Using the equation, predict the GPA score of a person with a math SAT score of 650.(d) Using the equation, predict the GPA score for a person with a math score of 800.

According to the Bureau of Labor Statistics, the mean salary for registered nurses in Kentucky was $57,688. The distribution of salaries is assumed to be normally distributed with a standard deviation of $5,879. Someone would like to determine if registered nurses in Ohio have a greater average pay. To investigate this claim, a sample of 192 registered nurses is selected from the Ohio Board of Nursing, and each is asked their annual salary. The mean salary for this sample of 192 nurses is found to be $58,016.005.  1. Completely describe the sampling distribution of the sample mean salary when samples of size 192 are selected. 2. What conjecture has been made? 3. Using the distribution described in part a, what is the probability of observing a sample mean of 58,016.005 or more? 4. Based on the probability found, what conclusion can be reached?