Which of the following is in the solution set of y < 5x + 3
a. (7,34)
b. (10,54)
c. (7,45)
d. (9,58)

We conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B.

Step-by-step explanation:

We are given that Location A was observed for 18 days and location B was observed for 13 days.  

On average, location A sold 39 of these items with a sample standard deviation of 8 and location B sold 49 of these items with a sample standard deviation of 4.

Let = true mean number of sales at location A.

= true mean number of sales at location B

So, Null Hypothesis, :  or       {means that the true mean number of sales at location A is greater than or equal to the true mean number of sales at location B}

Alternate Hypothesis, :  or      {means that the true mean number of sales at location A is fewer than the true mean number of sales at location B}

The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviations;

                        T.S. =    ~

where, = sample average of items sold at location A = 39

= sample average of items sold at location B = 49

= sample standard deviation of items sold at location A = 8

= sample standard deviation of items sold at location B = 4

= sample of days location A was observed = 18

= sample of days location B was observed = 13

Also,    =  = 6.64

So, test statistics  =    ~  

                               =  -4.14

The value of t test statistics is -4.14.

Now, at 0.01 significance level the t table gives critical value of -2.462 at 29 degree of freedom for left-tailed test.

Since our test statistics is less than the critical values of t as -2.462 > -4.14, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B.