Question

In: Operations Management

Your company has entered a new area, which is demographically similar to the area where you...

Your company has entered a new area, which is demographically similar to the area where you do business. The mean for sales each day in your current areas is $2000. You randomly selected 25 daily sales in the new area. The sample mean for this group is $2100 with a standard deviation of $250. At α = 0.05.

a.    Test to see if the average sale in the new area is different than the average sale in the current area.

b.    One of the directors is concerned that the sales in this new area may be higher. Test if the concern is valid?

Solutions

Expert Solution

a. vs

As n is less than 30 and population varaince not known we will use t distribution

The t-critical values for a two-tailed test, for a significance level of ?=0.05 are

tc?=?2.064 and tc?=2.064

Graphically

As t value is not in rejection region we fail to reject null hypothesis

b.

a. vs

As n is less than 30 and population varaince not known we will use t distribution

The t-critical value for a right-tailed test, for a significance level of ?=0.05 is

tc?=1.711

Graphically

As t statistics falls in the region region we reject the null hypothesis


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