Final answer:
The t-score for a 95% confidence interval with 16 degrees of freedom is approximately 2.120. The 95% confidence interval for the mean price of the digital phone is approximately $264.37 to $287.27.
Step-by-step explanation:
To answer the student's question: Justin is interested in buying a digital phone. He visited 17 stores at random and recorded the price of the particular phone he wants. The sample of prices had a mean of 275.82 and a standard deviation of 9.54. (a) What t-score should be used for a 95% confidence interval for the mean, μ, of the distribution? We first need to determine the degrees of freedom, which is the sample size minus one. In this case, 17 - 1 = 16 degrees of freedom. For a 95% confidence interval with 16 degrees of freedom, using a t-distribution table or calculator, we find the t-score that corresponds to a two-tailed test with the critical area of 0.025 in each tail, since the 95% confidence level refers to the middle 95% of the distribution. The t-score is approximately 2.120. (b) To calculate a 95% confidence interval for the mean price of this model of digital phone, the formula is: mean ± (t-score * (standard deviation / √(sample size))). This results in 275.82 ± (2.120 * (9.54 / √(17))).
The calculated confidence interval is then approximately $11.45, so the interval goes from $264.37 to $287.27.