Question

A research service estimates that the mean annual consumption of fresh market tomatoes by a person in the US is atleast 21 pounds. You doubt this claim. A simple random sample of 23 people in the US has a mean annual consumption of fresh market tomatoes of Xbar=19 pounds and a standard deviation of 4 pounds. Assume the pop. is normally distributed. Construct the appropriate hypothesis and conduct the test at the 1% level of significance. Based on the Critical Value approach is there enough evidence to reject the claim?

Answer 1

Solution:-

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

Null hypothesis: u > 21
Alternative hypothesis: u < 21

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 = 0.83406
DF = n - 1

D.F = 22
t = (x - u) / SE

t = - 2.398

t_critical = 2.508

Rejection region is t < - 2.508

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 - 2.398

Thus the P-value in this analysis is 0.013.

Interpret results. Since the P-value (0.013) 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 mean annual consumption of fresh market tomatoes by a person in the US is atleast 21 pounds.