Chapter 7

 

1.       Give brief answers to each of the following questions.

a.       What is the number t* with exactly probability 0.025 falling above it in the t distribution with 10 degrees of freedom?

b.       What critical value t* would you use in a 90% one-sample t confidence interval based on 20 observations?

c.       The one-sample t-statistic based on 15 observations takes the value t=3. Between what two levels from Table E does the P-value lie if the test is one-sided?

d.       Between what two levels does the P-value of the t statistic in ( c ) lie if the test is two-sided?

 

2.       A milk processor monitors the number of bacteria per milliliter in raw milk received for processing. A random sample of 10 one-milliliter specimens from milk supplied by one producer gives the following data: 5370,  4890,  5100,  4500,  5260,  5150,  4900,  4760,  4700,  4870

a.       Give a 90% confidence interval for the mean bacteria count per milliliter in this producer’s milk.

b.       What assumptions are required by the method you used in ( a )? How would you verify these assumptions? (You need not actually attempt to verify the assumptions.)

 

3.       The amount of wax deposited on the outside surface of waxed paper bags during production may vary  

 from the amount deposited on the inside surface. A sample of 25 bags is measured. For each bag,

 the wax concentration in pounds per square foot is determined on the inside and outside. The

 difference (outside minus inside) is calculated for each bag. The mean and standard deviation of

 these 25 differences are  = 0.093 and s = 0.723. Is there good evidence that the mean

 concentrations on the two surfaces are not equal?

 

4.       The reaction times of subjects to a stimulus in an experiment on visual perception are not normally distributed. A few very slow reactions give the distribution a long right tail. The experimental psychologist wants to determine whether the mean reaction time is less than 5 milliseconds based on 8 observations. Should she use a t test? Explain your answer.

 

5.       In an experiment to study the effect of the spectrum of the ambient (surrounding) light on the growth of plants, tobacco seedlings were divided at random into two groups of 8 plants each. The plants were grown in a greenhouse under identical conditions except for lighting. The experimental group was grown under blue light, the control group under natural light. Here are the data on stem growth in millimeters:

                                           Control Group           Experimental

4.3      4.2                       3.1    2.9

3.9    4.1                       3.2    3.2

                                     4.1    4.2                       2.7    2.9

3.8    4.1                         3.0    3.1

      Give a 90% confidence interval for the amount by which the blue light reduces stem growth during  

       this period.

 

6.       A study of the effect of eating sweetened cereals on tooth decay in children compared 73 children (Group 1) who ate such cereals regularly with 302 children (Group 2) who did not. After three years the number of new cavities was measured for each child. The summary statistics are:

                                 Group     n            s 

                                   1          73    3.41   3.62

                                   2         302   2.20   2.67

a.       The researchers suspected that sweetened cereals increase the mean number of cavities. Is there significant evidence for this suspicion at the 1% level?

b.       Does your result depend heavily on the shape of the distribution of cavity counts? Does it depend heavily on any other fact?