I need help with this as I have to round the decimal answers to at least 3 places, unless otherwise, but I wanted to see If I am doing it correctly as I am using the R coding program to solve the question.

Cell Phone bills in the United States are normally distributed with a mean $89.97 and an unknown standard deviation. It has been claimed that the Big X phone company has bills which are, on average, higher than the national mean. A random sample of some Big X customers found the following cell phone bills (in $): 95.73, 89.78, 102.88, 110.32, 110.32, 100.37, 92.35, 89.10, 89.92, 98.50, 91.19 So, we assume that our sample comes from a normal population with unknown mean of y and an unknown standard deviation of o. We would like to test whether the mean cell phone bill for Big X is greater than 89.97. The null hypothesis is thus Ho:=89.97 . We will test this against the alternative Ha - We want to test at the 6% level. Let x = the sample mean and s = the sample standard deviation. a) What should the alternative hypothesis, Ha , be? O Ha: H89.97 O Ha: H=89.97 O Ha: H#89.97 b) What is the formula for your test statistic? X-89.97 x-89.97 OT= V11 OT = x-89.97 X-89.97 OT= S 10 OT= X-6% c) What value does your test statistic, T, take on with the sample data? d) What type of probability distribution does your test statistic, T, have? O norma O Cauchy Ot O Chi-Squared O binomial e) How many degrees of freedom does T have? f) Calculate the critical value, tstar, for your test. (positive value) g) For what values of your test statistic, T, is the null hypothesis rejected? O T > tstar O T > tstar/2 or T tstar or T 14, \"#14, or u=4%) What is the formula for your test statistic? (You can call it T, formula means symbolic.) What value does your test statistic take on with the sample data? What type of probability distribution does T have? How many degrees of freedom does T have? Calculate the critical value for your test? (call it tstar) Note: tstar is negative) For what values of your test statistic is the null hypothesis rejected? (bigger than? or smaller than?) Calculate the p-value for this test. Is the null hypothesis rejected? (Y /N) Why? If we 600 4% level tests, then about how many times would we make a Type I error? Create a 96% condence interval for the J ane's true HC based upon this data. F\"-"~\"'F\" (new 5199'! #3 hemoglobin count - HC > x > (xbar (S # HO: mu = 14 = mul > mu0 #a Ha: mu #b t xbar # Sample mean of the data [1] 13.1 > t #d t has a t distribution with n-1 of > n - 1 #e degrees of freedom [1] 9 > alpha tstar tstar [1] -1.972653 > #g Rejected if t > pt (t, n- 1) # h p-value. This t is value of t formula part c [1] 0. 1434665 > #i Do not reject as t not > . 04 #k > tetstar# [1] FALSE > 600*. 04 #j type(I) errors in 800 4% level tests. [1] 24 > alpha tstarc c(xbar - tstarc*s/sqrt(n), xbar + tstarc*s/sqrt(n)) #k 96% confidence interval [1] 11. 19294 15. 00706