Question

Departmental Store Agora claims that their mean weekly sales of Aerosol were at most 2,400 packages over the past 6 months and population distribution is unknown. The manager wants to check if the sales have decreased in recent times. He obtained a random obtained sample of sales data from 61 stores and found that the sample mean is 3,593 packages with sample standard deviation 4919. At 7% significance level, using critical value approach see if the claim is true or not.

Answer 1

There is enough statistical evidence to suggest that the department's claim is not true

Explanation:

The mean weekly sales μ₀ ≤ 2,400 packages

The period over which the weekly sales were measured = Over the last 6 months

The number of stores in the sample, n = 61 stores

The sample mean,
`\overline x` = 3,593

The sample standard deviation, s = 4919

The significance level = 7% = 0.07

The critical value approach

The null hypothesis, H₀; μ ≤ μ₀

The alternative hypothesis, Hₐ; μ > μ₀

The test statistic is given as follows;

`t=\frac{\bar{x}-\mu }{(s)/(√(n))}`

We get;

`t=(3,593-2,400)/((4,919)/(√(61))) \approx 1.894`

With df = n - 1 = 61 - 1 = 60 at 7% significant level, from a graphing calculator the critical-t, = 1.495598

The p-value at the test statistic is between 0.01 and 0.005

Given that the p-value is less than the significant level, and the test statistic is larger than the critical-t we reject the null hypothesis, that the mean weekly aerosol sale is less than 2,400 packages.

Therefore, there is sufficient statistical evidence to suggest that the departments claim is not true and the mean sales of Aerosols have increased to more than 2,400 packages