Question

A survey of 36 Websites selling men’s Levi jeans in the U.S. revealed that the average price of men’s Levi jeans is $47.99 with a standard deviation of $9.80. a. What is the point estimate for the population average price of men’s Levi jeans? b. What is the 98% confidence interval to estimate the true price of men’s Levi jeans? c. A clothing store wants to temporarily lower the price of men’s Levi jeans at its store to increase customer traffic. The new, lower price must be less than the average price of men’s Levi jeans in order to increase sales. The store is considering pricing the Levi jeans at $42.99, $44.81, or $47.00. Which of the three prices do you recommend? Explain.

Answer 1

Question (a)

Point estimate for the populations average price of men's Levi jeans is the mean value or average price which is $47.99 here

Question (b)

Confidence interval is given by X +_- z * / n

Here X is sample mean = $47.99

is population standard deviation = $9.8

n is sample size = 36

Z-value will be obtained by the following table in the attached image below

Half of 0.98 is 0.49 so we look for the value 0.49 in the table and find the corresponding z-score

Here Z-score of 2.33 has an area of 0.4901.

So the approximate z-score is 0.4901

So Confidence interval is X +_- z * / n

= 47.99 +_- 2.33 * 9.8 / 36

= 47.99 +_- 2.33 * 9.8 / 6

= 47.99 +_- 3.8057

= (47.99 - 3.8057 , 47.99 + 3.8057)

So Confidence interval is (44.184 , 51.796)

Question (c)

We need to find the respective Z-score and then the p-values to see which p-value is higher among the three options

Z-score = (a - ) / / n

Here a values are three options given to us

= 47.99

= 9.8

n = 36

Now for option $42.99

Z-score = (42.99 - 47.99 ) / (9.8/ 36)

= -5 / 1.633

= -3.0612

Now calculate the p-value from the z-table attached below in the image

The corresponding p-value is 0.00111

Now for option $44.81

Z-score = (44.81 - 47.99 ) / (9.8/ 36)

= -3.18 / 1.633

= -1.946

Now calculate the p-value from the z-table attached below in the image

The corresponding p-value is 0.02559

Now for option $47

Z-score = (47 - 47.99 ) / (9.8/ 36)

= -0.99 / 1.633

= -0.606

Now calculate the p-value from the z-table attached below in the image

The corresponding p-value is 0.27093

Clearly the p-value is high in the case of $47 which is the recommended option