A swine producer wants to know if the average weight of his pigs is different from the breed average of 230 lb.  He selects a random sample of 16 weights from pigs in his herd and calculates a sample mean of 220 lb and a sample standard deviation of 25 lb.  Assume that he wants to detect departure from 230 lb in either direction and that he uses a significance level of 0.10.  Calculate the value of the test statistic needed to test the null hypothesis.

Construct a large-sample 90% confidence interval for the true population proportion if the sample estimate of p is 0.30.  The number of observations in the sample is 100.

Assuming that n1 = n2, find the sample sizes needed to estimate (μ1 – μ2) correct to within 2.5 with probability 0.90.  From prior experience we know that σ1 = 18 and σ2 = 16.

In a factorial experiment, when the dfifference between the mean levels of factor A depends on the different levels of factor B, we say that factors A and B interact.

Professors in the Department of Animal Sciences want to estimate the average length of time it takes students to complete a class project correct to within 5 hours with a 98% level of confidence.  Determine the sample size needed to estimate the average length of time required to complete the project to within 5 hours with a 98% level of confidence.  They do not know the standard deviation of the times, but they remember that last year the shortest amount of time needed to complete the project was 5 hours and the longest amount of time was 29 hours.

Suppose x has a binomial probability distribution with n = 400 and p = 0.70.  Use the normal approximation to the binomial to find P (X > 300).

Suppose x has a binomial probability distribution with n = 200 and p = 0.60.  Use the normal approximation to the binomial to find P (X 

The owner of a herd of cows wants to determine the influence of the ages of his cows on the amount of calving difficulty that occurs in his herd.  He constructs the following table:                             Age of Cow (in years)                                           0-2     3-5     6-10     over 10   Total No difficulty     40      35       20          5            100 Difficult birth   35      45       15          5            100 Total                  75      80       35        10           200   What is the probability that a randomly selected cow either has calving difficulty or is less than 3-years-old?

Suppose we want to estimate the average height of all young growing maple trees found on a certain nursery.  We select a random sample of 25 trees and measure their heights.  The sample mean is 75 inches and the sample standard deviation is 8 inches.  Construct a 90% confidence interval for the population mean (μ).  Assume that any necessary assumptions have been met.

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. Perform the calculations needed to determine if the sample size of n = 150 is large enough for large-sample confidence interval procedures to be valid.  Is the sample size large enough?