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If the variation within sample means is large relative to the variation between the samples, it indicates that there is a real difference between the population means.

Suppose x has a binomial probability distribution with n = 200 and p = 0.70.  Use the normal approximation to the binomial to find P (X > 150).

Owners of a breed of beef cattle noted for heavy birth weights and calving difficulty would like to prove that the mean birth weight of their breed is less than 85 lb.  In other words, they want to test:      Ho:  µ = 85 lb      Ha:  µ < 85 lb They obtain a random sample of 169 birth weights of calves from this breed and find a sample mean of 83 lb and a sample standard deviation of 10 lb.  Using a significance level of 0.05, which one of the following statements is the correct conclusion?

A plant scientist wants to determine the average yield (in bushels per acre) of brand X corn in Ohio.  Five thousand Ohio corn fields are planted using brand X.  The plant scientist is able to obtain data for the yields of 500 of these 5,000 fields.  The average yield of these 500 fields planted to brand X is 175 bushels per acre.  What is the population of interest to the plant scientist?

The Kimberly Clark Corporation wants to determine how many tissues a box of Kleenex should contain.  Researchers determine that 60 is the average number of tissues used by a typical person during a cold.  Suppose a random sample of 100 Kleenex users yielded a sample mean of 56 tissues and a sample standard deviation of 10 tissues used during a typical cold.  Kimberly Clark wants to test:    Ho:  μ = 60 tissues    Ha:  μ < 60 tissues using a significance level (α) = 0.05. Should Kimberly Clark reject or not reject the null hypothesis?  Why?

We want to test the hypothesis that the mean number of credit hours taken per semester by OSU undergraduates is less than 16 hours.  Therefore, we obtain a random sample of credit hours for 49 students. The sample mean is 15 hours and the sample standard deviation is 4 hours.  We want to test:    Ho:  μ = 16 hours    Ha:  μ < 16 hours using a significance level (α) = 0.01. What is the critical value needed to test the null hypothesis in this problem?

Parking at a large university has become a big problem.  University administrators are interested in determining the average parking time (i.e., the average length of time it takes students to find a place to park on campus) of the students.  An administrator inconspicuously follows 250 students and carefully records their parking times.  Identify the experimental units in this study of parking times.

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).

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.

The symbol for the variance of a population is _______.