In Gallup's Annual Consumption Habits Poll, telephone interviews wereconducted for a random sample of 1014 adults aged 18 and over. One ofthe questions was, "How many cups of coffee, if any, do you drink on anaverage day?" The following table shows the results obtained (Gallup website, August 6, 2012). Number of Cups per day Number of responses 01234 or more 36526419391101 Define a random variable x = number of cups of coffee consumed on anaverage day. Let x= 4 represent four or more cups.a. Develop a probability distribution for x. b. Compute the expected value of x.c. Compute the variance of X.d. Suppose we are only interested in adults who drink at least onecup of coffee on an average day. For this group, let y = the numberof cups of coffee consumed on an average day. Compute theexpected value of y and compare it to the expected value of x.

Twenty-eight college faculty at Acme Looniversity who volunteered for a fitness program were divided into low-fitness and high-fitness groups based on a physical examination. The subjects then took a Personality Factor Questionnaire. Below are the data for the "ego strength" measurement based on the questionnaire. Acme Looniversity Data Group Fitness Sample size Average Standard deviation 1 Low 14 4.6 0.69 2 High 14 6.4 0.43 Assuming the data for Group 1 and 2 are independent of each other and are both normally distributed, compute a 90% confidence interval for the difference between the two means. Round your answer to 3 decimal places. What conclusion can you draw? Group of answer choices (-2.173,-1.427), Group 1 is bigger (-1.923,-1.677), Group 2 is bigger (-2.173,-1.427), Group 2 is bigger (-1.923,-1.677), no conclusion (-1.923,-1.677), Group 1 is bigger

A union of restaurant and foodservice workers would like to estimate the mean hourly wage, u, of foodservice workers in the U.S. this year The mean hourly wage last year was $8.08, and there is good reason to believe that this year's value is different from last year's. The union decides to do a statistical test to see if the value has indeed changed. The union chooses a random sample of this year's wages, computes the mean of the sample to be $7.78, and computes the standard deviation of the sample to be $1.20. Based on this information, complete the parts below. (a) What are the null hypothesis H. and the alternative hypothesis H₁ that should be used for the test? H₂ : O H₁ :0 (b) Suppose that the union decides not to reject the null hypothesis. What sort of error might it be making? (Choose one) ▼ (c) Suppose the true mean hourly wage for foodservice workers in the U.S. this year is $8.08. Fill in the blanks to describe a Type I error. A Type I error would be (Choose one) when, in…

A random survey of enrollment at 10 community colleges across the United States yielded the following figures: 2523; 1707; 5420; 2835; 1129; 5452; 2360; 1448; 2958; and 4110. What is the 99% Error Bound (EBM) of the population mean?