Suppose x has a binomial probability distribution with n = 150 and p = 0.60.  We want to determine if it is appropriate to use the normal approximation to the binomial.  Which one of the following statements is true?

We want to test the hypothesis that the mean yield of a particular variety of corn is less than 150 bushels per acre.  Therefore, we obtain the yields of a random sample of 20 corn fields in which this variety was planted. The average yield of the sample of fields was 140 bushels per acre with a standard deviation of 10 bushels per acre.  We want to test:    Ho:  μ = 150 bushels/acre    Ha:  μ < 150 bushels/acre using a significance level (α) = 0.10. Should we reject or not reject the null hypothesis?  Why?

A national organization has been working with electric companies throughout the US to find sites for large windmills to generate electric power.  Wind speeds must average more than 21 miles per hour (mph) for a site to be acceptable.  Recently, the organization conducted tests at a particular site where windmills are under construction.  Based on a sample of n = 40 wind speed recordings (taken at random intervals) at the site, the wind speeds averaged 23 mph with a standard deviation of 3.9 mph.  To determine whether the site meets the organization’s requirements, they want to test:    Ho:  μ = 21 mph    Ha:  μ > 21 mph using a significance level (α) = 0.01. Calculate the value of the test statistic needed to test the null hypothesis.

We want to use a confidence interval to estimate the proportion of students in the College of Food, Agricultural, and Environmental Sciences that are female.  What sample size would be necessary if we want to estimate the true proportion of female students correct to within 0.03 with probability 0.95?  In an earlier small-scale pilot study, we obtained an estimate of the proportion of female students (p) that was equal to 0.48.

Find the probability of an observation lying more than z = 1.67 standard deviations above the mean.

Health care issues are receiving a greal deal of attention in both the academic and political arenas.  A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance.  The ages (in years) of 9 uninsured senior citizens were as follows: Senior Citizen Age 1 65 2 70 3 64 4 84 5 74 6 72 7 87 8 79 9 80 Find the median age of these 9 senior citizens.

Outliers are typically due to which of the following causes

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.