Question

1)An online stock trading company makes part of their revenue from clients when the clients trade stocks therefore, it is important to the company to have an good idea of how many trades its clients are making in a given year. In a sample of 120 clients of an online stock trading company, the average number of trades per year was 82 with a standard deviation of 16. If you were to test the hypothesis that the average number of trades per year is different than the previous year when the average number of trades was 85 (using the 5% level of significance), what is p-value for this test? (please round your answer to 4 decimal places)

2)Nationwide, the mean amount of sales each week at Lowe’s store is normally distributed with a mean of $5.2 million with a standard deviation of $0.86 million. Lowe’s has decided to close 15% of its stores, and has chosen amount of sales as the criterion on which the decision will be based (they are going to close the 15% of the stores with the lowest sales). How much in sales does a store have to have in order to not be closed? (please express your answer in millions and round your answer to 2 decimal places)

Answer 1

Solution: 1)An online stock trading company makes part of their revenue from clients when the clients trade stocks therefore, it is important to the company to have an good idea of how many trades its clients are making in a given year. In a sample of 120 clients of an online stock trading company, the average number of trades per year was 82 with a standard deviation of 16. If you were to test the hypothesis that the average number of trades per year is different than the previous year when the average number of trades was 85 (using the 5% level of significance), what is p-value for this test?

Answer: The null and the alternative hypotheses are:

In order to find the P-value, we need to know the test statistic. So let's first find the test statistic.

The test statistic is given below:

  

  

  

Now let's find the P-value.

P-value

Using the standard normal table, we have:

  

Therefor the P-value of the test is

2)Nationwide, the mean amount of sales each week at Lowe’s store is normally distributed with a mean of $5.2 million with a standard deviation of $0.86 million. Lowe’s has decided to close 15% of its stores, and has chosen amount of sales as the criterion on which the decision will be based (they are going to close the 15% of the stores with the lowest sales). How much in sales does a store have to have in order to not be closed?

Answer: We are given:

We have to find the z value corresponding to probability 0.15. We can use NORMSINV() function in excel to find the z value.

Now, we have

Now to find the Sales that a store should have in order to not get closed is given:

Therefore a store should have $4.31 million sales in order to not be closed.

  

Answer: