Question

Energy drinks are very popular on college campuses and in most cases, they have a lot of caffeine in them. Some students think that brand X is superior to other brands and wanted to measure the amount of caffeine in brand X to see if it was higher than the advertised amount. The cans say that there is 160 mg of caffeine per 16 ounces can. The students measured the total amount of caffeine in 30 randomly selected cans of brand X to see if it was higher than listed.

A.) Are these samples in this data set paired samples, independent samples, or a single sample?

B.) What kind of test would be best to use? (Mann-whitney, Paired t-test, Wilcoxon signed ranks, Two sample t-test, Anderson Darling, One sample t-test, the sign test, or a two-sample t-test)

C.) Using population parameters µ, θ, or p, identify the null and alternative hypothesis.

D.) What should the alpha (α) value be for this study?

E.) Which of the choices best matches your interpretation of the results for this statistical test?

The results were significant so we reject the null hypothesis and support the alternative

The results were not significant so we fail to reject the null hypothesis

The results were not significant so we reject the null hypothesis and accept the alternative

The results were significant so we fail to reject the null hypothesis

record.number	caffeine
1	176.3
2	166.8
3	156.7
4	170.3
5	171.3
6	182.8
7	158.9
8	146.4
9	176.3
10	174.6
11	166.1
12	159.2
13	146.8
14	139.2
15	161.3
16	151.2
17	154.9
18	167.9
19	147
20	179.5
21	159.8
22	168.2
23	163
24	175.5
25	166.3
26	147.9
27	157.9
28	167.9
29	173.1
30	162.3

Answer 1

Answer a:

As we are comparing the label clam vs actual claim so it is single sampel test

Answer b:

As we are comparing the claim that the caffiene per can for single brand X so we can go with one sampel t test

Answer c:

Null hypothesis:

The cafffeine contians per can (16 ounce) is less than or equal to 160 mg

Alternate hypothesis:

The cafffeine contians per can (16 ounce) is higher than 160 mg

Answer d:

Now if we calculte the p value:

t = (mean of sample -mean of labeled )/ (stnadard deviaiton of sample /sqrt(sample size))

if we calculate the mean and standard deviation, 163.18 and 11.058 mg of caffeine per 16 ounce can

t = (163.18-160)/11.058/sqrt(30)

t =3.18/2.019 = 1.5751

If we see the p value at t value of 1.5751 it is 0.063041

So we can use the same here:

So at 95% confidence interval, we fail to reject the null hypothesis

So at alpha = 0.05 we fail to reject the null hypothesis

and higher value than 0.063041 alpha value we can reject the null hypothesis

alpha =0.05

Answer e:)

So correct answer is:

The results were not significant so we fail to reject the null hypothesis