Answer Happy

3. The number of calories in a 12-ounce can of non-diet cola isnormally distributed with a mean 150 calories and an unknownstandard deviation. John Pemberton claims that the true mean isactually higher than 150 calories. A random sample of ten 12-ouncecans of non-diet cola was selected and the number of calories foreach follows:143.4, 153.6, 168.2, 164.3, 150.8, 161.7, 149.9, 172.8, 144.0,146.6So, we assume that our sample comes from a normal population withunknown mean of 𝜇 and an unknown standard deviationof 𝜎. We would like to test whether the mean number ofcalories in a 12-ounce can of non-diet cola is greater than150.The null hypothesis is thus H0:𝜇=150. We will testthis against the alternative Ha.We want to test at the 3% level.Let x = the sample mean and s = the sample standarddeviation.
a) What should the alternative hypothesis, Ha,be?
* Ha:𝜇=3%
* Ha:𝜇≠150
* Ha:𝜇>150
* Ha:𝜇<150
* Ha:𝜇=150
b) What is the formula for your test statistic?
T =
T =
T =
T =
T =
c) What value does your test statistic,T, take on with thesample data? d) What type of probability distribution does your teststatistic,T, have?
* normal
* binomial
* t
* Cauchy
* Chi-Squared
e) How many degrees of freedom does T have?
f) Calculate the critical value, tstar, for your test.(positivevalue)
g) For what values of your test statistic, T, is the nullhypothesis rejected?
* T > tstar/2 or T < -tstar/2
* T < tstar
* T > tstar or T < -tstar
* T > tstar
* |T - tstar| < .03
h) Calculate the p-value for this test.
i) Is the null hypothesis rejected? (Y/N)
j) If we ran 900, 3% level tests then about how many times wouldwe make a Type I error?
k) Create a 97% confidence interval for the mean of the numberof calories in a can of non-diet cola: ( _____ , _____)
l) Copy your R script or any other comments for the above intothe text box here.