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

The value of the test statistic is 1.667

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. =
`(Xbar-\mu)/((\sigma)/(√(n) ) )` ~ N(0,1)

where, Xbar = sample mean = $8,250

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

n = sample size = 64

So, test statistics =
`(8,250-8,000)/((1,200)/(√(64) ) )`

= 1.667

Therefore, the value of test statistics is 1.667 .