10.9 A car magazine is comparing the total repair costs incurredduring the first three years on two sports cars, the T-999 and the XPY.Random samples of 45 T-999s and 51 XPYS are taken. All 96 cars are3 years old and have similar mileages. The mean of repair costs forthe 45 T-999 cars is $3300 for the first 3 years. For the 51 XPY carsthis mean is $3850. Assume that the standard deviations for the twopopulations are $800 and $1000, respectivelya. Construct a 99% confidence interval for the differencebetween the two population meansb. Using a 1% significance level, can you conclude that suchmean repair costs are different for these two types of cars?c. What would your decision be in part b if the probability ofmaking a Type I error were zero? Explain

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Asked Nov 7, 2019
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10.9 A car magazine is comparing the total repair costs incurred
during the first three years on two sports cars, the T-999 and the XPY.
Random samples of 45 T-999s and 51 XPYS are taken. All 96 cars are
3 years old and have similar mileages. The mean of repair costs for
the 45 T-999 cars is $3300 for the first 3 years. For the 51 XPY cars
this mean is $3850. Assume that the standard deviations for the two
populations are $800 and $1000, respectively
a. Construct a 99% confidence interval for the difference
between the two population means
b. Using a 1% significance level, can you conclude that such
mean repair costs are different for these two types of cars?
c. What would your decision be in part b if the probability of
making a Type I error were zero? Explain
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10.9 A car magazine is comparing the total repair costs incurred during the first three years on two sports cars, the T-999 and the XPY. Random samples of 45 T-999s and 51 XPYS are taken. All 96 cars are 3 years old and have similar mileages. The mean of repair costs for the 45 T-999 cars is $3300 for the first 3 years. For the 51 XPY cars this mean is $3850. Assume that the standard deviations for the two populations are $800 and $1000, respectively a. Construct a 99% confidence interval for the difference between the two population means b. Using a 1% significance level, can you conclude that such mean repair costs are different for these two types of cars? c. What would your decision be in part b if the probability of making a Type I error were zero? Explain

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Expert Answer

Step 1

The provided information for the T-999 and XPY sports cars are:

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Sample size(n) 45 Sample mean ()=3300 Population standard devition(o)800 Sample size(n,) 51 Sample mean () = 3850 Sample standard devition (o2)=1000

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Step 2

(a)

The formula to calculate the confidence interval for differences in population mean is:

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2 ()2x

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Step 3

The required value of z can be ...

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Z=Z0.01 2 2.576 (Using z-table)

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