Recently, a price war has developed among retailers selling Brand X denim jeans. A major chain buyer wishes to estimate the mean price of these jeans during this period to compare it to the normal selling price of $20.00. A random sample of 7 major retailers produces a mean retail price of $13.50 with a standard deviation of $3.50. A 80% confidence interval for the true mean retail price of Brand X jeans during the price war is:

Question

Recently, a price war has developed among retailers selling Brand X denim jeans. A major chain buyer wishes to estimate the mean price of these jeans during this period to compare it to the normal selling price of $20.00. A random sample of 7 major retailers produces a mean retail price of $13.50 with a standard deviation of $3.50. A 80% confidence interval for the true mean retail price of Brand X jeans during the price war is:

(10.93, 16.07)

(11.60, 15.40)

(8.46, 18.54)

(11.81, 15.19)

(10.00, 17.00)

Answer 1

(11.60, 15.40)

Answer 2

To calculate the 80% confidence interval for the true mean retail price of Brand X jeans during the price war, we can use the formula:

Confidence Interval = mean ± margin of error

First, let's calculate the margin of error:

Margin of Error = (critical value) * (standard deviation / √sample size)

Since we want a 80% confidence interval, the critical value can be found using the t-distribution table for a sample size of 7 and a confidence level of 0.80. From the table, the critical value is approximately 1.895.

Now, let's plug in the values into the formula:

Margin of Error = 1.895 * (3.50 / √7)

Margin of Error ≈ 1.895 * (3.50 / 2.6458)

Margin of Error ≈ 1.895 * 1.3230

Margin of Error ≈ 2.51

Next, we can calculate the confidence interval:

Confidence Interval = $13.50 ± $2.51

Confidence Interval ≈ ($10.99, $16.01)

Therefore, the 80% confidence interval for the true mean retail price of Brand X jeans during the price war is (10.99, 16.01).

The correct answer is option: (10.93, 16.07)

Answer 3

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

First, we need to find the critical value for an 80% confidence level. This can be determined using a t-distribution table or calculator. For a sample size of 7 and a confidence level of 80%, the critical value is approximately 1.895.

Next, we need to calculate the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard deviation is $3.50 and the sample size is 7.

Standard Error = $3.50 / √7 ≈ $ 1.32

Now, we can calculate the confidence interval:

Confidence Interval = $13.50 ± (1.895 * $1.32)
= $13.50 ± $2.50
= ($11.00, $16.00)

Therefore, the correct answer is:

(11.00, 16.00)

Answer 4

CI80 = mean ± 1.28(sd/√n)

With your data:

CI80 = 13.50 ± 1.28(3.50/√7)

I'll let you take it from here to choose your answer.