Question

The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,250 per day. From past information, it is known that the standard deviation of the population is $1,200.
The value of the test statistic is:_________.

Answer 1

Answer:

The value of the test statistic is 1.667

Step-by-step explanation:

We are given that the sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. For this a random sample of 64 days of sales was selected. It was found that the average was $8,250 per day. From past information, it is known that the standard deviation of the population is $1,200.

We have to determine whether or not the advertising campaigns have been effective in increasing sales.

Let, Null Hypothesis, $H_0$ : $\mu$ = $8,000 {means that the advertising campaigns have not been effective in increasing sales}

Alternate Hypothesis, $H_1$ : $\mu$ > $8,000 {means that the advertising campaigns have been effective in increasing sales}

The test statistics that will be used here is One sample z-test statistics;

             T.S. = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, Xbar = sample mean = $8,250

                $\sigma$  = population standard deviation = $1,200

                 n = sample size = 64

So, test statistics = $\frac{8,250-8,000}{\frac{1,200}{\sqrt{64} } }$

                            = 1.667

Therefore, the value of test statistics is 1.667 .