1. In studying many different brands of pet food, a pet store manager found some
ID: 3040473 • Letter: 1
Question
1. In studying many different brands of pet food, a pet store manager found some data on cost per serving of each brand:
0.22 0.28 0.36 0.40 0.48 0.49 0.50 0.50 0.52 0.52 0.53 0.54 0.55 0.59 0.62 0.62 0.62 0.65 0.67 0.68 0.74
a) Calculate the following for this sample: sample mean, sample median, sample variance, standard deviation, standard error of the sample mean, range, and coefficient of variation. (You can use Excel)
Calculate a 95% confidence interval about the sample mean. Be sure to use the correct distribution in your calculations (t or Z?)Try to show your work (if you are doing this by calculator) – you can try to use the equation editor in Word; or you can type in equations in Word as best you can; or you can work it out by hand and scan your work into Word (make sure it’s legible).You can also use Excel to calculate the confidence interval, but be sure to choose the correct one; then cut and paste part of the Excel spreadsheet into Word.
Suppose the average price per serving in the previous year was 0.48. Test the hypothesis that the mean price per serving has increased since last year (ie. Test that the mean of this sample is greater than 0.48).Include your null and alternative hypothesis, whether or not you reject the null hypothesis and why you reject or do not reject the null hypothesis (ie. use the results of the t-test to support your answer).Use an alpha level of 0.05. Unfortunately, Excel does not do a one-sample t test for you, so you’ll have to do this one by hand and calculator, but Excel has helped with calculation of mean and variance for you (see above re showing your work). You can also use Excel to determine critical t values or p values for calculated t statistics.
Explanation / Answer
Calculation
M = 0.527619
t = 2.09
sM = (0.1302652/21) = 0.03
= M ± t(sM)
= 0.527619 ± 2.09*0.03
= 0.527619 ± 0.05929592
M = 0.527619, 95% CI [0.46832308, 0.58691492].
You can be 95% confident that the population mean () falls between 0.46832308 and 0.58691492.
0.22 0.28 0.36 0.4 0.48 mean 0.527619 0.49 median 0.53 0.5 std dev 0.130265 0.5 COV 0.246893 0.52 0.52 0.53 0.54 0.55 0.59 0.62 0.62 0.62 0.65 0.67 0.68 0.74Related Questions
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