Question

The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 12 supermarkets from Region 1 had mean sales of 79.8 with a standard deviation of 8.8. A random sample of 17 supermarkets from Region 2 had a mean sales of 85.2 with a standard deviation of 8.3. Does the test marketing reveal a difference in potential meal sales per market in Region 2? Use a signifiance level of a = 0.02 for the test. State the null and alternative hypotheses for the test and find the test statistic.

Answer 1

The null hypothesis is
`H_o: \mu_1 = \mu_2`

The alternative hypothesis is
`H_1 : \mu_1 \\e \mu_2`

The test statistics is
`t = -1.667`

Explanation:

From the question we are told that

The first sample size is
`n_1 = 12`

The first sample mean is
`\= x_1 = 79.8`

The first standard deviation is
`\sigma _1 = 8.8`

The second sample size is
`n_2 = 17`

The second sample mean is
`\= x_2 = 85.2`

The second standard deviation is
`\sigma _2 = 8.3`

The null hypothesis is
`H_o: \mu_1 = \mu_2`

The alternative hypothesis is
`H_1 : \mu_1 \\e \mu_2`

Generally the test statistics is mathematically represented as

`t = \frac{\= x_ 1 - \= x_2 }{ \sqrt{ (\sigma_1^2 )/(n_1 ) +(\sigma_2^2 )/(n_2) } }`

=>
`t = \frac{ 79.8 - 85.2 }{ \sqrt{ (8.8^2 )/(12) +( 8.3^2 )/(17) } }`

=>
`t = -1.667`