# Testing of hypothesis and regression problems

3.3

The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of 10 batteries is subjected to an accelerated life test by running them continuously at an elevated temperature until failure, and the following lifetimes (in hours) are obtained: 25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3 and 25.7.

a) The manufacturer wants to be certain that the mean battery life exceeds 25h. What conclusions can be drawn from these data (use ?alpha? = 0.05)

b) Construct a 90% two-sided confidence interval on mean life in the accelerated test.

3.8

The diameters of aluminum alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 in. A random sample of 25 rods has an average diameter of 0.5046 in.

a) Test the hypothesis that mean rod diameter is 0.5025 in. Assume a two-sided alternative and use ?alpha? = 0.05

b) Find the P-value for this test.

c) Construct a 95% two-sided confidence interval on the mean rod diameter

3.21

An experiment was conducted to investigate the filling capability of packaging equipment at a winery in Newberg, Oregon. Twenty bottles of Pinot Gris were randomly selected and the fill volume (in ml) measured. Assume that fill volume has a normal distribution. The data are as follows: 753, 751, 752, 753, 753, 753, 752, 753, 754, 754, 752, 751, 752, 750, 753, 755, 753, 756, 751, and 750.

a) Do the data support the claim that the standard deviation of fill volume is less than 1 ml? Use ?alpha? = 0.05

b) Find a 95% two-sided confidence interval on the standard deviation of fill volume.

c) Does it seems reasonable to assume that fill volume has a normal distribution?

12.8

Use the data in Table 12-10

Height, inches 70 63 72 60 66 70 74 65 62 67

Weight, lbs 155 150 180 135 156 168 178 160 132 145

a) Plot the data

b) Calculate the regression line of Y on X

c) Calculate the regression line of X on Y

d) Why do the two regression lines intersect at one point?

13.0

Data of hockey players

Height (inches) Speed (miles per hour)

5?11 67

5?8 70

5?10 57

5?8 67

6?1 44

5?9 65

6?4 51

6?3 54

5?7 68

6?0 59

a) Analyze data using problem solving questions from class

b) Include an intro (example: This project is to?), graphs, a summary, conclusion Example: smaller players skate faster?)

#### Solution Summary

The solution gives detailed answers to students t test, chi square test, z test, correlation and regression analysis problems. Step by step procedure is given with interpretations of the results obtained.