Justin is interested in buying a digital phone. He visited 16 stores at random and recorded the price of the particular phone he wants. The sample of prices had a mean of 262.49 and a standard deviation of 27.57.

A) What t-score should be used for a 95% confidence interval for the mean, μ, of the distribution?
t* = ()

B) Calculate a 95% confidence interval for the mean price of this model of digital phone:
(Enter the smaller value in the left answer box.)

() to ()

Following are the solution to the given points:

For point a:

Determine the t score that is used to calculate a confidence interval for the distribution's mean "".

The t-score formula is

Here,

Therefore,  

According to the t distribution table,    As a result, the t score for a confidence interval again for distribution's mean =.

For point b:

Determine a confidence interval for the mean price of this model of the digital phone.

Formula for confidence interval:

Here,  

Therefore,

As a result, the confidence interval again for the mean price of this model of digital phone is .

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a) t = 2.131

b) The 95% confidence interval for the mean price of this model of digital phone is (247.80, 277.18)

Step-by-step explanation:

Sample size = n = 16

Sample mean = x = 262.49

Sample Standard deviation = s = 27.57

Part a) Value of t-score

We have to construct a confidence interval for the mean. Since, value of population standard deviation is unknown, and value of sample standard deviation is known, we will use t-distribution to find the confidence interval.

Degrees of freedom = df = n - 1 = 16 - 1 = 15

The critical t-value which we have to use should be checked again 15 degrees of freedom and 95% confidence level. From the t-table this value comes out to be:

t = 2.131

Part b) Confidence Interval

The formula to calculate the confidence interval is:

Here, is the critical t-score we found in the previous part. Using the values in the formula, we get:

Therefore, the 95% confidence interval for the mean price of this model of digital phone is (247.80, 277.18)

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step-by-step explanation: