Lesson 2 – there are 4 questions total complete solutions correct answers key

Lesson 2 – there are 4 questions total complete solutions correct answers key

1) A motivational program was designed to increase the number of hours each student who took it studied per week. Eight randomly selected students were involved in the program. The table below shows the number of hours each student studied per week before the taking motivational program and after taking the program.

Before program :  8 , 12,10,12,5,10,10,12

after program: 12,11,14,15,8,15,9,6

At the 10% level of significance, can it be concluded the motivational program increased the average number of hours students studied per week? Formulate and test the appropriate hypotheses. Use the critical value approach.

Assume that the population of paired differences has a normal distribution.

2)

A random sample of 16 students showed that the variance in the number of hours they spend studying for a final exam was 25 hours2.

a. Construct a 95% confidence interval for the population variance and standard deviation of hours spent studying. Assume the population of hours spent studying is normally distributed.

b. Test, at the 5% level of significance, whether the population standard deviation of hours spent studying is less than 10. Use the critical value approach.

3)  Three Different brands of pain relief medication are available for minor aches and pains. It is of interest to know whether then mean time to relieve the pain differs from brand to brand. To find out, twelve individuals with minor aches and pains were randomly assigned to one of the three brands. The time to relieve the pain (in minutes) for each individual is provided in the table below.

Brand A -  10min, 12 min, 15 min, 14 min

Brand B- 15 min, 22 min, 25 min, 19min

Brand C - 20min, 25min, 20 min, 11 min

 Given that the necessary assumptions are satisfied, can it be concluded, at the 2.5% level of significance, that not all mean times to relieve pain are equal? Formulate and test the appropriate hypotheses. Use the critical value approach.

4)  A manufacturer of exercise bicycles is studying the relationship between the number of months an exercise bicycle has been owned and the length of time it was used last week. Data for a random sample of 7 owners are provided in the table below.

Months owned (X)     /   Hours used last week (y)

14                                /    6

8                                    / 8

5                                    / 7

3                                   / 9

10                                 / 6

4                                    / 8

12                                  / 7

a) construct a scatter diagram for these data with Months owned on the x and hours used on the y axis.

b) describe the general pattern of the relationship between the two variables

c) calculate the least square regression line with hours used as the dependent variable and months owned as the independent variable.

    note. express a and b to 4 decimal places of accuracy/

d) Plot the regression line on the scatter diagram you constructed in part a

e) Can it be concluded that the slope of the regression line is negative? Formulate and test the appropriate hypothesise  at the 5% significance level. Use the Critical value approach.

f) Construct a 95% confidence interval for B. 

g) Interpret the numerical value of b in the sample regression line. What does it mean in the context of this question?

h) use the equation of the regression line to predict hours used last week if an exercise bicycle has been owned for 11 months. 

    note. express your answer to 2 decimal places of accuracy