The normal approximation to a binomial probability distrubtion is reasonably good even for small sample sizes (say, n as small as 10) when p = 0.5 and the distribution of X is therefore symmetric about its mean.

What assumption is required for estimating the population mean when we have small samples of n < 30?

Consider the following probability distribution:                                                                                  x         -2       -1       0        1        2                                                                                  P(x)  .12     .09     .25     .30     .24                                                                                  Find the mean of this probability distribution.

Assume that a 95% large-sample confidence interval for (p1 – p2) turns out to be (0.20, 0.30).  What is the correct interpretation of this confidence interval?

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets – Kroger, Giant Eagle, and Meier.  Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets.  In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item                          Kroger    Giant Eagle    Meier     1) Big Thirst Towel      $1.21       $1.49          $1.59 2) Post Golden Crisp    2.78         2.99            3.35 3) Tylenol Tablets         5.98         5.29            5.98           .                              .              .                   .           .                              .              .                   . 59) Colgate Shave       0.94         1.10            1.19 60) Kidney Beans        0.45          0.56            0.38                                                                                   The results of the Analysis of Variance for this experiment are as follows: Source           df       SS            MS          F     Total                       222.21     Supermarket              2.64       1.32       39.23 Item                        215.59       3.65     108.54 Error                           3.97      0.0337                                                                                What are the correct degrees of freedom for total, supermarket, item, and error, respectively?

If n < 30, we can use a small-sample hypothesis test about the population mean.  What assumption must we make in order to use this procedure?

A college professor wants to estimate the difference in mean test scores of students who have taken his statistics and genetics classes in the past 10 years.  He selects a random sample of 20 student records from the statistics course and a random sample of 22 student records from the genetics course.  These two samples were independent random samples.  The study provided the results shown in the table below.  Construct a 95% confidence interval for the true difference in population means of these two populations of students.   Statistics Genetics Sample size 20 22 Sample mean 78 75 Sample standard dev. 10 12

Which one of the following is not an assumption required for small-sample estimation of (μ1 – μ2)?

The peak shopping time at Rod’s Western Palace is between 8:00 and 11:00 am on Saturday mornings.  The store manager randomly selected 50 customers last Saturday morning and observed their shopping habits.  The manager recorded the number of items purchased by each customer and the total time each customer spent in the store.  Identify the type of variables recorded by the manager.

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