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A golf pro wants to determine if Titleist Pro V1 golf balls (1) travel farther, on average, than Callaway Chrome Soft golf balls (2)

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A golf pro wants to determine if Titleist Pro V1 golf balls (1) travel farther, on average, than Callaway Chrome Soft golf balls (2).  A robot hits 9 of each ball, selected at random, and the distance traveled is measured.  Assume the distances traveled are normally distributed. 

The average distance traveled by the 9 Titleist Pro V1 golf balls is 261.1 yards with standard deviation 10 yards, and the average distance traveled by the 9 Callaway Chrome Soft golf balls is 249.3 yards with standard deviation 12 yards. 

 

1)Which test should the golf pro use to determine if Titleist Pro V1 golf balls travel a longer average distance than Callaway Chrome Soft golf balls? 

 

Sign Rank Test

 

t test for proportions

 

paired z test for means

 

t test for means

 

paired t test for means

 

z test for means

 

z test for proportions

 

2) Which alternative hypothesis should the golf pro use to determine if Titleist Pro V1 golf balls travel a longer average distance than Callaway Chrome Soft golf balls? 

 

HA:p1−p2≠0

 

HA:μ1−μ2≠0

 

HA:p1−p2<0

 

HA:μ1−μ2>0

 

HA:p1−p2>0

 

HA:μ1−μ2<0

 

3)The p-value of the test is 0.0188.  What is the conclusion of the test at α=.10? 

 

a)Fail to reject H0. There is sufficient evidence at α=.10 to conclude that Titleist Pro V1 golf balls travel a longer average distance than Callaway Chrome Soft golf balls. 

 

b)Reject H0. There is sufficient evidence at α=.10 to conclude that Titleist Pro V1 golf balls travel a longer average distance than Callaway Chrome Soft golf balls. 

 

c)Fail to reject H0. There is insufficient evidence at α=.10 to conclude that Titleist Pro V1 golf balls travel a longer average distance than Callaway Chrome Soft golf balls. 

 

d)Reject H0. There is insufficient evidence at α=.10 to conclude that Titleist Pro V1 golf balls travel a longer average distance than Callaway Chrome Soft golf balls. 

 

4)A 90% confidence interval for μ1−μ2 is: (2.7, 20.9).  Interpret the interval. 

 

a)We are 90% confident that the average distance traveled by Callaway Chrome Soft golf balls is between 2.7 and 20.9 yards longer than the average distance traveled by Titleist Pro V1 golf balls.

 

b)At the 90% level of confidence, there is insufficient evidence to conclude that Titleist Pro V1 golf balls travel a farther average distance than Callaway Chrome Soft golf balls.  

 

c)We are 90% confident that the average distance traveled by Titleist Pro V1 golf balls is between 2.7 and 20.9 yards longer than the average distance traveled by Callaway Chrome Soft golf balls.

 

 

Information for questions 13-18:

An insurance company determines that a linear relationship exists between the cost of fire damage in major residential fires and the distance from the house to the nearest fire station.  A sample of 20 recent fires in a large suburb of a major city was selected. For each fire, the following variables were recorded: 

x= the distance between the fire and the nearest fire station (in miles)
y= cost of damage (in dollars)

The distances between the fire and the nearest fire station ranged between 0.6 miles and 6.2 miles. 

 

1)The correlation between cost and distance is 0.842.  What is the critical value for testing if the correlation is significant at α=.01? 

Give the exact value from the critical value table. 

 

2)The correlation between cost and distance is 0.842.  Test if the correlation is significant at α=.01. 

 

No, the correlation is not significant because 0.842 does not exceed the critical value.

 

Yes, the correlation is significant because 0.842 does not exceed the critical value.

 

No, the correlation is not significant because 0.842 is smaller than 1.

 

No, the correlation is not significant because 0.842 exceeds the critical value.

 

Yes, the correlation is significant because 0.842 exceeds the critical value.

 

3)What is the regression equation for predicting cost of damage from the distance between the fire and the nearest fire station when the slope is 4919, and the y-intercept is 10278 ?

 

y^=4919x+10278

 

y=4919x+10278

 

y=10278x+4919

 

y^=10278x+4919

 

y=4919+10278

 

4)Predict the cost of damage for a house that is 3 miles from the nearest fire station.  

Type either a numerical value or not appropriate.