Question

An advertising executive wants to determine if a new billboard placed in a city caused sales of her product to increase. To do this, she selects random stores that sell the product on the billboard and compares the amount sold in one business cycle before the billboard was placed to the sales of one business cycle after. Suppose that data were collected for a random sample of 10 stores, where each difference is calculated by subtracting the number of units sold in thousands before the billboard was placed from the number of units sold in thousands after the billboard was placed. Assume that the numbers are normally distributed. The executive uses the alternative hypothesis Ha:μd>0. Using a test statistic of t≈6.537, which has 9 degrees of freedom, determine the range that contains the p-value.

Answer 1

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

The correct option is the first and the last option

Explanation:

From the question we are told that

The sample size is n = 10

The null hypothesis is
`H_o :  \mu_d  =  0`

The alternative hypothesis is
`H_a :  \mu_d  >  0`

The test statistics is
`t \approx 6.537`

The level of significance is
`\alpha  = 0.05`

Generally the p-value is mathematically represented as

`p-value  =  P(t >  6.537 )`

From z-table
`P(t >  6.537 ) = 0`

So

`p-value  =  0`

From the value obtained we see that
`p-value < \alpha` hence we reject the null hypothesis that the true mean difference between the number of units sold after the billboard was placed and the number of units sold before the billboard was placed is equal to zero

Thus we conclude that

Based on the results of the hypothesis test, there is not enough evidence at the level of significance(0.05) to suggest that the true mean difference between the number of units sold after the billboard was placed and the number of units sold before the billboard was placed is greater than zero