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We want to test the following null and alternative hypotheses about a population proportion: Ho:  p = 0.20 Ha:  p ≠ 0.20 We observe 300 successes in a sample of 1,000 observations.  Assume that it is valid to use large-sample procedures in this problem. Calculate the test statistic needed to test the null hypothesis.

The average height cows of a certain breed is 54 inches and the standard deviation of the heights is 8 inches.  Fifteen percent of the cows are expected to be less than X inches tall.  Find the value of X.

The weights of 25 lambs (in pounds) in a flock of sheep are as follows: 68     73     66     76     86     74     61     89     65     90 69     92     76     62     81     63     68     81     70     73     60     87     75     64     82 Construct a stem-and-leaf display using the first digit as the stem and the second digit as the leaf.  Based on the stem-and-leaf display, the median for this set of weights is __________ lb.

The following table shows litter sizes for sows in four breeds of pigs. Yorkshire     Landrace     Hampshire     Duroc      8                   9                   8                 7     10                  9                   7                 8     11                10                   8                 9     11                10                   9                 7       9                  8                                                 49                46                 32               31 – treatment totals     9.8               9.2               8.0              7.5 – sample means     The correct degrees of freedom for total, treatments, and error in the Analysis of Variance table for this problem are ____________.                                                                                    

The grades of 8 students on an exam were as follows: Student Grade 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79     Find the standard deviation of the grades of these 8 students.

Suppose that a 94% confidence interval for μ turns out to be (60 inches, 80 inches).  To make more useful inferences from the data, it is desired to reduce the width of the confidence interval.  What action should we take to reduce the width of the confidence interval?

Assume that a scientist conducts a 2 x 3 factorial experiment.  The Analysis of Variance table is shown below: Source          df          SS               MS               F     Total             17        1.73397 Factor A        1         0.10125       0.10125        23.0375 Factor B        2         0.81195       0.405975       92.3720 A x B             2         0.76803       0.384015       87.3754 Error            12        0.05274        0.004395                                                                                          Based on this analysis and a significance level of α = 0.05, what should the scientist conclude?

Breeders of the Longhorn breed of cattle select to increase the length of the horns (i.e., the distance from the tip of one horn to the tip of the other horn).  A Longhorn breeder would like to know the average length of horns found on Longhorn cattle in Texas.  A random sample of 144 Longhorn cattle yields a mean horn length of 72 inches and a standard deviation of 15 inches. Estimate the population mean for length of horns of Longhorn cattle in Texas using a 95% confidence interval.  What is the correct interpretation of the confidence interval that you derived?

We are interested in estimating the average driving time of students who commute to Ohio State.  How many students who commute need to be included in our sample to order to be 98% confident that the estimated mean driving time will be within 4 minutes of the true population mean driving time if the standard deviation of the driving times is 8 minutes?

Assume that we want to test the null hypothesis that the correlation between two variables is 0 vs. the alternative hypothesis that the correlation between these two variables is positive.  Based on a random sample of n = 20 observations, we calculate the sample correlation coefficient of r = 0.50.  Using a significance level of 0.05, which one of the following statements represents the correct conclusion?