# 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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41 views help_outlineImage Transcriptionclose10.9 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 fullscreen
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Step 1

The provided information for the T-999 and XPY sports cars are: help_outlineImage TranscriptioncloseSample size(n) 45 Sample mean ()=3300 Population standard devition(o)800 Sample size(n,) 51 Sample mean () = 3850 Sample standard devition (o2)=1000 fullscreen
Step 2

(a)

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

Step 3

The required value of z can be ...

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