Blog

In order to compare the means of two populations, independent random samples are selected from each population, with the results shown in the table below.  Use these data to construct a 98% confidence interval for the difference in the two population means.   Sample 1 Sample 2 Sample size 400 400 Sample mean 5,275 5,240 Sample standard dev. 150 200

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. State the null and alternative hypothesis that the researcher wants to test.

A dairy producer in Ohio wants to determine if the average milk production of her Holstein cows is greater than 18,000 lb of milk per lactation.  Therefore, she obtains a random sample of n = 100 milk production records from her herd and calculates a sample mean of 18,500 lb and a sample standard deviation of 3,500 lb. State the null and alternative hypotheses that she wants to test.

We are interested in comparing the mean supermarket prices of two leading colas in the Columbus area.  Assume that we have independent random samples of prices of six-packs at 8 supermarkets.  The data are shown in the following table: Supermarket      Brand 1       Brand 2  1                             $2.25          $2.30 2                               2.47            2.45 3                               2.38            2.44 4                               2.27            2.29 5                               2.15            2.25 6                               2.25            2.25 7                               2.36            2.42 8                               2.37            2.40 _______________________________________ Mean                       $2.3125       $2.3500 Standard deviation  $0.1007       $0.0859 _______________________________________ Find a 98% confidence interval for the difference in mean price of Brand 1 and Brand 2, assuming that these are independent random samples.

A bottling company needs to produce bottles that will hold 12 ounces of liquid for a local beer maker.  Periodically, the company receives complaints that their bottles are not holding enough liquid.  To test this claim, the bottling company randomly samples 15 bottles and finds the average amount of liquid held by the 15 bottles is 11.90 ounces and the standard deviation is 0.20 ounces. Suppose the test results indicated that the null hypothesis should be rejected, and, as a result, the company shut down their machine for inspection.  However, a thorough examination revealed that the machine was filling the bottles correctly.  From a statistical point of view, which one of the following is true?

Which one of the following graphical methods is not used to describe qualitative data?

Medical research has shown that a certain type of chemotherapy is successful 70% of the time when used to treat skin cancer.  Suppose 5 skin cancer patients are treated with this type of chemotherapy.  Let X equal the number of patients out of 5 who are cured.  The probability distribution for the number of patients out of 5 who are cured is given in the following table:                                                                                         X             0           1           2           3           4           5     P (X)    0.002   0.029   0.132    0.309    0.360    0.168       Find σ2 = E [(X – μ)2].

According to a study conducted at a university, many adults have experienced lingering “fright” effects from a scary movie or TV show they saw as a teenager.  In a survey of 150 college students, 39 said that they still experience “residual anxiety” from a scary movie or TV show. Construct a 95% confidence interval to estimate the true population proportion of college students who experience “residual anxiety” from a scary movie or TV show.

The computer science department wants to estimate the average length of time it takes students to complete a computer project correct to within 5 hours with probability 0.96.  They do not have an estimate of the standard deviation of the times, but they remember that last year the shortest time needed to complete the project was 6 hours and the longest time was 36 hours.  Given this information, an appropriate estimate of the standard deviation of the length of time required to complete the computer project would be:

The body weight in pounds (variable X) and fleece weight in pounds (variable Y) of a random sample of four ewes are as follows: Body weight, lb (X)            Fleece weight, lb (Y)           140                                            9           145                                          10           155                                          10           160                                          12                                                                                      Calculate the covariance between body weight and fleece weight.