Weights are recorded for 500 Labrador Retriever dogs.  The type of data being collected is ____________ data.

An animal scientist is interested in determining the proportion of ewes that give birth to twins.  Rather than examine the records for all ewes in the United States, he randomly selects 500 ewes and finds that 220 of them gave birth to twins.  He constructs a 99% large-sample confidence interval to estimate the true population proportion of ewes that give birth to twins.  The correct interpretation of the confidence interval that he derived is:

An insurance company states that their claim office is able to process all death claims for cattle within 5 working days.  Recently there have been several complaints that it took longer than 5 days to process a claim.  Top management sets up a statistical test with a null hypothesis that the average time for processing a claim is 5 days and an alternative hypothesis that the average time for processing a claim is greater than 5 days.  After completing the statistical test, it is concluded that the average exceeds 5 days.  However, it is eventually learned that the mean processing time really is 5 days.  What type of error occurred in the statistical test?

An animal scientist wants to estimate the proportion of heifers that require assistance when giving birth to their first calves.  Based on previous research, the animal scientist believes that the proportion of heifers that require assistance is 0.20.  How large of a sample does the animal scientist need in order to obtain an estimate of p that is correct to within 0.05 with probability equal to 0.90?

In a pizza takeout restaurant, the following probability distribution was obtained.  The random variable X represents the number of toppings for a large pizza.                                                                                      x             0          1          2          3          4          P(x)          0.30     0.40     0.20     0.06     0.04          Calculate the variance of this discrete probability distribution.

If we roll a single die, the sample points are 1, 2, 3, 4, 5, or 6.  Consider the following two events:      Event A:  toss an even number on the die      Event B:  toss a number less than or equal to 3 on the die List the sample points that would be included in the union of events A and B (i.e., A U B).

A study was conducted to determine whether a student’s final grade in a high school math class is linearly related to his or her performance on the math ability test administered before college entrance.  The math test scores and final grades for a random sample of 10 students are shown below. Final Grade in Math Class (X)          Math Ability Test Score (Y) 65                                                             39 78                                                             43 52                                                             21 82                                                             64 92                                                             57 89                                                             47 73                                                             28 98                                                             75 56                                                             34 75                                                             52   What are the correct null and alternative hypotheses if we want to test that these two variables are positively correlated?

The Environmental Science & Technology journal reported on a study of contaminated soil in The Netherlands.  A total of 81 soil specimens were sampled, dried, and analyzed for the contaminant cyanide.  The cyanide concentation (in milligrams per kilogram, mg/kg, of soil) of each soil specimen was determined using an infrared microscopic method.  The samples had a mean cyanide level of 95 mg/kg and a standard deviation of 50 mg/kg.  The authors of the journal article tested the hyothesis that the true mean cyanide level in the soil in The Netherlands was less than 100 mg/kg using a significance level of α = 0.10. Calculate the value of the test statistic needed to test this hypothesis.

A swine producer reads a report stating that the average litter size in the US is 7.8 pigs per litter.  However, he feels that the average litter size on his farm is not 7.8 pigs/litter (he wants to detect departure in either direction from the hypothesized mean of 7.8 pigs/litter).  To test his hypothesis, he reviews his records for the past year and randomly selects 16 litters, which averaged 8.0 pigs/litter.  The standard deviation is 1 pig/litter. State the null and alternative hypothesis.

If we roll a single die, the sample points are 1, 2, 3, 4, 5, or 6.  Consider the following two events:      Event A:  toss an even number on the die      Event B:  toss a number less than or equal to 3 on the die Calculate the probability of the union of events A and B:  P( A U B).