Question

A supermarket is trying to decide whether to accept or reject a shipment of tomatoes. It is impossible to check all the tomatoes for size, but they desire an average weight of 8 ounces (they neither want too large nor too small).

(a) State the hypotheses.

(b) A random sample of 25 tomatoes yields an average weight of 7.65 ounces and a standard

deviation of 1.15 ounces. Calculate the test statistic and the p-value.

(c) Would you reject H0, or fail to reject H0 at 5% level of significance?

(d) Should the supermarket reject the shipment? Explain.

(e) To what type of error are you subject to?

Answer 1

Solution:-

a)

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

Null hypothesis: u = 8
Alternative hypothesis: u 8

Note that these hypotheses constitute a two-tailed test.

b)

Formulate an analysis plan. For this analysis, the significance level is 0.05. 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 = 0.23

DF = n - 1

D.F = 24
t = (x - u) / SE

t = - 1.52

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.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 24 degrees of freedom is less than -1.52 or greater than 1.52.

Thus, the P-value = 0.142

Interpret results. Since the P-value (0.142) is greater than the significance level (0.05), we cannot reject the null hypothesis.

c) Do not reject the null hypothesis at 5% level of significance.

d) No, market should not reject the shipment.

e) We are subjected to type II error.