Exam 11: Inference About a Population

In estimating the population mean with the population standard deviation unknown, if the sample size is 16, there are 8 degrees of freedom.

In order to interpret the p -value associated with hypothesis testing about the population mean m , it is necessary to know the value of the test statistic.

The t- distribution is used in a confidence interval for a mean when the actual standard error is not known.

Applicants' Grades The grades of a sample of 10 applicants, selected at random from a large population, are 71, 86, 75, 63, 92, 70, 81, 59, 80, and 90. {Applicants' Grades Narrative} Construct a 90% confidence interval estimate for the population variance.

The degrees of freedom for the test statistic for m when s is unknown is:

When the population standard deviation is ____________________ and the population is normal, the test statistic for testing hypotheses about m is the t -distribution with n - 1 degrees of freedom.

Science Quiz Scores Consider the hypotheses H ₀: s ² = 20 vs. H ₁: s ² > 20. Assume that Science scores on a 25-point quiz for a random sample of 5 students were drawn from a normal population. These were: 18, 16, 10, 13, and 23. {Science Quiz Scores Narrative} Test the hypotheses at the 10% significance level.

A condition of using the chi-squared test statistic for testing the variance is that the population random variable have a normal distribution.

Tire Rotation The manager of a service station is in the process of analyzing the number of times car owners rotate the tires on their cars. She believes that the average motorist rotates his or her car's tires less frequently than recommended by the owner's manual (two times per year). In a preliminary survey she asked 14 car owners how many times they rotated their cars' tires in the last 12 months. The results are 1, 1, 2, 0, 3, 3, 0, 1, 0, 1, 2, 3, 3, and 1. {Tire Rotation Narrative} What condition is required in order to analyze this data using a t -test?

Science Quiz Scores Consider the hypotheses H ₀: s ² = 20 vs. H ₁: s ² > 20. Assume that Science scores on a 25-point quiz for a random sample of 5 students were drawn from a normal population. These were: 18, 16, 10, 13, and 23. {Science Quiz Scores Narrative} Estimate the population variance with 90% confidence.

Mystic Pizza Mystic Pizza in Mystic, Connecticut, advertises that they deliver your pizza within 15 minutes of placing an order or it is free. A sample of 25 customers is selected at random. The average delivery time in the sample was 13 minutes with a sample standard deviation of 4 minutes. {Mystic Pizza Narrative} What is the required condition of the technique used in the previous question?

The t -statistic has two variables: the sample ____________________ and the sample ____________________.

Single Mothers' Ages A random sample of 10 single mothers was drawn from a Obstetrics Clinic. Their ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24 years. {Single Mothers' Ages Narrative} Estimate the population mean with 90% confidence.

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t- distribution equal n - 1 because we lose one degree of freedom by using the:

If the sampled population is nonnormal, the t -test of the population mean m is still valid, provided that the condition is not extreme.

A random sample is drawn from a normal distribution with mean m and variance s ² . The random variable ( n - 1)S² \ s ² has a chi-squared probability distribution with n degrees of freedom.