3. The number of calories in a 12-ounce can of non-diet cola is normally distributed with a mean 150 calories and an unk

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3 The Number Of Calories In A 12 Ounce Can Of Non Diet Cola Is Normally Distributed With A Mean 150 Calories And An Unk 1 (303.04 KiB) Viewed 29 times

3. The number of calories in a 12-ounce can of non-diet cola is normally distributed with a mean 150 calories and an unknown standard deviation. John Pemberton claims that the true mean is actually higher than 150 calories. A random sample of ten 12-ounce cans of non-diet cola was selected and the number of calories for each follows: 143.4, 153.6, 168.2, 164.3, 150.8, 161.7, 149.9, 172.8, 144.0, 146.6 So, we assume that our sample comes from a normal population with unknown mean of μ and an unknown standard deviation of o. We would like to test whether the mean number of calories in a 12-ounce can of non-diet cola is greater than 150. The null hypothesis is thus Ho:μ=150. We will test this against the alternative Ha. We want to test at the 3% level. Let x = the sample mean and s = the sample standard deviation. 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? X-150 OT= OT=_S OT= X-150 OT= /9 X-150 S 10 OT=X-3% S X-150 S 10 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 Cauchy Ot Obinomial O Chi-Squared O normal 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? OT<tstar OT> tstar T> tstar or T < -tstar O IT-tstar| < .03 OT> tstar/2 or T < -tstar/2
h) Calculate the p-value for this test. i) Is the null hypothesis rejected? (Y/N) Y N j) If we ran 900, 3% level tests then about how many times would we make a Type I error? k) Create a 97% confidence interval for the mean of the number of calories in a can of non-diet cola: ( 1) Copy your R script or any other comments for the above into the text box here.