The sales manager of a food company wants to determine if the weekly sales of 16

Question

The sales manager of a food company wants to determine if the weekly sales of 16 ounce packages of frozen broccoli has increased since last year. The mean weekly number of sales per store was 2, 400 packages last year. The sales manager set the following hypotheses to test. H_0: mu = 2400 H_1: mu > 2400 Available sales data are from 400 stores. Assume that this data set is a random sample. The sample mean is 2, 450 and the sample standard deviation is 800. For the significance level of 10%, find the critical value. a. 2451.2 b. 2465.6 c. 2348.8 d. 2334.4 e. 2450

Explanation / Answer

Solution:-

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

Null hypothesis: = 2400

Alternative hypothesis: > 2400

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.10. 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 = 40

DF = n - 1 = 400 - 1

D.F = 399

t = (x - ) / SE

t = 1.25

tcritical = 1.284

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

The observed sample mean produced a t statistic test statistic of 1.25. We use the t Distribution Calculator to find P(t > 1.25) = 0.106

Interpret results. Since the P-value (0.106) is greater than the significance level (0.10), we cannot reject the null hypothesis.

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