A random sample of n = 16 professors from a university has been selected; salaries have been plotted on the following Q-Q plot. qqplot If we created a 95% confidence interval for salaries to be ($99,881, $171,172), how would we interpret that interval? Since n = 16 > 15, we can use the CLT to say we are 95% sure that all professors' salaries at this university are between $99,881 and $171,172. Since n = 16 > 15, we can use the CLT to say we are 95% sure the average of all professors' salaries at this university is between $99,881 and $171,172. We actually can't be 95% sure the average professor salary is in the interval, since the salaries are right-skewed and n = 16 < 30.

Question

04-04-2020
Mathematics

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A random sample of n = 16 professors from a university has been selected; salaries have been plotted on the following Q-Q plot. qqplot If we created a 95% confidence interval for salaries to be ($99,881, $171,172), how would we interpret that interval? Since n = 16 > 15, we can use the CLT to say we are 95% sure that all professors' salaries at this university are between $99,881 and $171,172. Since n = 16 > 15, we can use the CLT to say we are 95% sure the average of all professors' salaries at this university is between $99,881 and $171,172. We actually can't be 95% sure the average professor salary is in the interval, since the salaries are right-skewed and n = 16 < 30.

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mtosi17 mtosi17 · Answer 1 · 2020-04-05T02:31:14+02:00

Answer:

The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance.

The conclusion we can make is that there is 95% of probability that the mean of the population (professor's average salary) is within $99,881 and $171,172.

Step-by-step explanation:

This is a case in which, from a sample os size n=16, a confidence interval is constructed.

The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance. In this case, the probability that the real mean is within the interval is 95%.