Questions: A random sample of 15 statistics textbooks has a mean price of 105 with a standard deviation of 30.25. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be us to construct a confidence interval. Assume the distribution of statistics textbook prices is not normally distributed A. Use the I-distribution. B. Use normal distribution C. Cannot use normal distribution or t-distribution

A random sample of 15 statistics textbooks has a mean price of 105 with a standard deviation of 30.25. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be us to construct a confidence interval. Assume the distribution of statistics textbook prices is not normally distributed

A. Use the I-distribution. B. Use normal distribution C. Cannot use normal distribution or t-distribution

Transcript text: A random sample of 15 statistics textbooks has a mean price of $\$ 105$ with a standard deviation of $\$ 30.25$. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be us to construct a confidence interval. Assume the distribution of statistics textbook prices is not normally distributed A. Use the I-distribution. B. Use normal distribution C. Cannot use normal distribution or t-distribution

Solution

Solution Steps

Step 1: Identify the Distribution

Given a random sample of 15 statistics textbooks with a mean price of $ \mu = 105 $ and a standard deviation of $ s = 30.25 $, we need to determine the appropriate distribution to use for constructing a confidence interval.

Since the sample size $ n = 15 $ is less than 30 and the distribution of statistics textbook prices is not normally distributed, we should use the t-distribution.

Step 2: Conclusion

Based on the analysis, the appropriate distribution to use for constructing the confidence interval is the t-distribution.