For small samples (n < 30), the sampling distribution of the sample mean depends on the particular form of the relative frequency distribution of the population being sampled.

According to a study conducted at a university, many adults have experienced lingering “fright” effects from a scary movie or TV show they saw as a teenager.  In a survey of 150 college students, 39 said that they still experience “residual anxiety” from a scary movie or TV show. Construct a 95% confidence interval to estimate the true population proportion of college students who experience “residual anxiety” from a scary movie or TV show.

An experiment is conducted to compare the starting salaries of male and female college graduates who find jobs.  Pairs are formed by choosing a male and a female with the same major and similar grade point averages.  Suppose a random sample of 10 pairs is formed in this manner and the starting annual salary of each person is recorded.  The differences within the pairs are obtained by subtracting the female salary from the male salary. The following results are obtained:      Mean difference in starting salaries = $400      Standard deviation of the difference in starting salaries = $435 Construct a 95% confidence interval for the true mean difference in starting salaries of the male and female graduates.

Find the standard deviation of a binomial probability distribution with a sample size of n = 20 and a probability of success of 0.40.

It seems reasonable to assume that ovulation rate and litter size in pigs would be positively correlated.  In other words, if a sow releases more eggs (i.e., ova) in a given estrus period, she will probably end up producing more pigs in her litter.  Number of eggs ovulated and litter size for a random sample of 6 sows are as follows: Number of Eggs, X       Number of Pigs Born, Y                14                                  7                15                                  7                16                                  9                17                                 10                17                                 10                17                                  11 Use the deterministic component of the straight-line probabilistic model to obtain the predicted litter size if a sow ovulates 16 eggs.

An animal scientist is interested in determining the proportion of ewes that give birth to twins.  Rather than examine the records for all ewes in the United States, he randomly selects 500 ewes and finds that 220 of them gave birth to twins.  He constructs a 99% large-sample confidence interval to estimate the true population proportion of ewes that give birth to twins.  The correct interpretation of the confidence interval that he derived is:

Suppose that a random sample of 100 measurements is selected from a population with a mean µ = 200 lb and a variance σ2 = 1,600 lb2.  What is the mean and standard deviation of the sampling distribution of the sample mean?

The average litter size in Ohio is approximately 8 pigs per litter.  Owners of a particular breed would like to prove that the mean litter size of their breed is greater than 8 pigs per litter.  Therefore, they want to test:      Ho:  μ = 8 pigs/litter      Ha:  μ > 8 pigs/litter They obtain a random sample of 100 litter size records from sows of this breed and find a sample mean of 8.4 pigs per litter and a sample standard deviation of 1 pig per litter.  They decide to use a significance level of α = 0.01. What is the appropriate test statistic needed to test the null hypothesis?

A bottling company needs to produce bottles that will hold 12 ounces of liquid for a local beer maker.  Periodically, the company receives complaints that their bottles are not holding enough liquid.  To test this claim, the bottling company randomly samples 15 bottles and finds the average amount of liquid held by the 15 bottles is 11.90 ounces and the standard deviation is 0.20 ounces. Suppose the test results indicated that the null hypothesis should be rejected, and, as a result, the company shut down their machine for inspection.  However, a thorough examination revealed that the machine was filling the bottles correctly.  From a statistical point of view, which one of the following is true?

The average height of a certain ornamental plant is 14 inches and the standard deviation of the heights is 2 inches.  Only 20% of the plants are expected to be less than X inches tall.  Find the value of X.