Suppose that 80% of the Holstein cows in the U.S. give birth to their calves with no calving difficulty.  We randomly select 7 Holstein cows from the population consisting of all Holstein cows in the U.S.  What is the probability that at least 5 of the 7 (i.e., 5 or more) cows in this sample will give birth to their calves with no calving difficulty?  To find the answer to this question, you can use the equation for the binomial distribution or a binomial probability table.

A litter of 5 pigs is produced.  What is the probability that exactly 3 of the 5 pigs will be females, assuming that the probability of a male pig is 1/2 and the probability of a female pig is 1/2?

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. Should the authors of the journal article reject the null hypothesis?  Explain.

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a school levy in a certain school district.  A random sample of 400 people of voting age is selected.  Results of the poll show that 240 of the 400 people polled plan to vote in favor of the school levy.  Perform the calculations needed to determine whether or not it would be appropriate to construct a large-sample confidence interval for the true population proportion.  What do you conclude (i.e., is it appropriate?

A scientist wants to estimate the true population proportion of mares that conceive when bred by AI.  She selects a random sample of 500 mares and finds that 300 of the 500 mares conceived when bred by AI.  The scientist knows that it is appropriate to construct a large-sample confidence interval for the true population proportion because

Find the probability of an observation lying more than z = 1.67 standard deviations above the mean.

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.

Find the probability of an observation lying more than z = 1.56 standard deviations below the mean.

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

A 2 x 4 factorial experiment is conducted to compare yields of 4 varieties of soybeans that are planted in rows either 15 inches or 30 inches apart.  Two plots of ground are randomly assigned to each combination of soybean variety and row spacing.  The yields of soybeans (in bushels per acre) are as follows:           Rows 1 2 3 4 15″ 45 46 47 46   46 46 48 43 30″ 35 41 42 39   32 39 38 41 The partially completed ANOVA table is as follows: Source df SS MS F Total   319.75     Variety   41.25 13.75 5.0 Row spacing   225 225 81.8 Variety x row spacing   31.5     Error   22 2.75   Should we reject or not reject the null hypothesis for the interaction between variety and row spacing?  Use a significance level of α = 0.05.