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For a fixed confidence coefficient, the width of the confidence interval increases as the sample size increases.

Scientists want to estimate the difference in twinning rate of two lines of beef cattle that have been selected for increased frequency of twin births.  Last spring, 40 of the 100 cows in Line 1 gave birth to twins.  In Line 2, 30 of the 100 cows gave birth to twins. Construct a 90% confidence interval for the true difference in population proportions of cows giving birth to twins in Lines 1 and 2.  In the interest of time, you can assume that the sample sizes are large enough that it is appropriate to use a large-sample confidence interval.

A box of Mr. Phipps Tater Crisps is supposed to contain 156 grams of potato chips.  On the side of the box it says “This package is sold by weight, not by volume.  Packed as full as practicable by modern automatic equipment, it contains full net weight indicated.  If it does not appear full when opened, it is because contents have settled during shipping and handling”.  Periodically, the Nabisco Company receives complaints that their boxes of Tater Crisps are not full (i.e., that they contain less than 156 grams of potato chips).  To test this claim, the Nabisco Company randomly samples 10 boxes and finds the average amount of potato chips held by the 10 boxes is 154 grams and the standard deviation is 30 grams. State the null and alternative hypotheses the Nabisco Company wishes to test.

A two-factor factorial experiment is conducted to compare litter sizes of Yorkshire and Landrace sows derived either from a line unselected for litter size or from a line that has gone through 15 years of selection for increased litter size.  Two sows of each breed are randomly selected from each line.  Their litter sizes are as follows:                                   Yorkshire       Landrace            Unselected line               8                     9                                        9                    10 Selected line                 11                    11                                      10                      9                                                                                     The partially completed ANOVA table is as follows:  Source             df             SS                MS            F  Total                              7.875 Line                               3.125            3.125       3.57 Breed Line x Breed Error                              3.500            0.875                                                                                       Find the F value for the line x breed interaction.

Starting salary and GPA of students who graduate from OSU are examples of ____________ data.

The Lantern wants to conduct an opinion poll to estimate the true population proportion of OSU students who think OSU will win the NCAA tournament this year in basketball.  How many students will the Lantern need to include in their sample to estimate the true population proportion to within 0.05 (i.e., B = 0.05) with probability equal to 0.95?  No prior estimates of p and q are available.

In the 1970’s it was generally assumed that the mean birth weight of Angus beef cattle was 75 lb.  A researcher believes that, due to selection for increased size and growth rate in Angus, the average birth weight is now greater than 75 lb.  He obtains a random sample of n = 144 birth weights of Angus calves and calculates a sample mean of 85 lb and a sample standard deviation of 10 lb. Calculate the test statistic need to test the null hypothesis.  Using the appropriate table and a significance level (α) = 0.05, find the critical value of the test statistic.  Should the researcher reject or not reject the null hypothesis?  Explain.

The Central Limit Theorem guarantees that the population is normally distributed whenever n is sufficiently large (n > 30).

A box of Mr. Phipps Tater Crisps is supposed to contain 156 grams of potato chips.  On the side of the box it says “This package is sold by weight, not by volume.  Packed as full as practicable by modern automatic equipment, it contains full net weight indicated.  If it does not appear full when opened, it is because contents have settled during shipping and handling”.  Periodically, the Nabisco Company receives complaints that their boxes of Tater Crisps are not full (i.e., that they contain less than 156 grams of potato chips).  To test this claim, the Nabisco Company randomly samples 10 boxes and finds the average amount of potato chips held by the 10 boxes is 154 grams and the standard deviation is 30 grams. Using a significance level of α = 0.05, find the rejection region for the test of the null hypothesis.

Assume that the mean length of time required to complete the Columbus Marathon was 4.5 hours.  Further assume that the standard deviation of the times required to complete the race was 0.50 hours.  The winning time was 2.3 hours.  Calculate the z-score for the runner with the winning time of 2.3 hours.  Based on this z-score, is this time of 2.3 hours an outlier?  Why or why not?