Dr. Spike is a big fan of Bojangles and is particularly interested in the popularity of its celebrated wingsdinner. Starting from January, he would visit the local Bojangles on randomly selected days. Upon eachvisit, he would ask the manager how many wings dinners were sold on the previous day. By the end ofMarch, he had visited Bojangles for a total of 31 times and thus collected 31 sale records of wingsdinners. It was found that the sample mean was 26.2 sales with a sample standard deviation of 12.8. He would liketo use this information to estimate the average number of wings dinner sold per day between January andMarch using a confidence interval.(This particular Bojangles sold 3872 wings dinners last year, but Dr. Spike does not know this.)

Which of the following facts isnotrelevant for evaluating whether or not a confidence interval for the mean number of wings dinners sold per day can be calculated using this data?

a.The number of sampled days is 32, which is a sufficient sample size for the confidence interval to be meaningful..

b.The days he visited were randomly selected, so the sample is representative of the population.

c.Since three sample standard deviations below the sample mean is negative (26.2-3*12.8 = -12.2), the distribution of wings dinner sales is positively skewed, and therefore not normal so the confidence interval will not be meaningful.

d.All of the above statements are relevant.

Ignoring any issues with the assumptions in the previous question, calculate a 95% confidence interval for the mean number of wings dinners sold per day based on the sample.

Please include all work, including the values of any variables used and the number of degrees of freedom, if relevant, in your response. Give your answer accurate to two decimal places.

Dr. Spike's rival, Dr. Drop, also was interested in the mean number of wings dinners sold at his local Bojangles. Using his own sample of size 44, he calculated a confidence interval of (26.7, 33.2). Which of the following is a correct interpretation of his confidence interval?

Select one:

a.If we randomly select a day, the probability that the number of wings dinners sold that day is between26.7 and 33.2 is 95%.

b.If many random samples of size 44from this Bojangles are selected, 95% of them will have true means between26.7 and 33.2 wings dinners sold per day.

c.We would fail to reject theH0:=30against the alternativeHA:30 using this sample.

d.If many random samples of size 44 from this Bojangles are selected, 95% of them will have sample means between26.7 and 33.2 wings dinners sold per day.