Question

(1 point) A certain type of soda has 200 calories in a one liter bottle, on average. A small simple random sample of such bottles has the following calorie measurements: 202 \ \ 205 \ \ 201 \ \ 202 \ \ 198 Four out of five measurements are over 200. Test the null hypothesis that the average is 200 calories (assuming measurements are Normally distributed). (a) What is the t-statistic? (Round to three decimal places.) (b) What is the P-value? (Round to three decimal places; calculator required.) (c) Are the data statistically significant? A. Yes. B. No. (d) Are the data sufficient evidence against the 200 calorie claim? A. Yes. B. No.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 200
Alternative hypothesis: u > 200

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 1.1225
DF = n - 1

D.F = 4
t = (x - u) / SE

t = 1.43

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 1.43.

Thus the P-value in this analysis is 0.113.

Interpret results. Since the P-value (0.113) is greater than the significance level (0.01), we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the average is 200 calories.

c) No, the data is not statistically significant.

d) No, data is not sufficient evidence against the 200 calorie claim.