Ex: In a crash test of 15 Honda Odyssey minivans, collision repair costs are fou

Question

Ex: In a crash test of 15 Honda Odyssey minivans, collision repair costs are found to have an approximately normal distribution with a sample mean of $1,786. Below is a 99% confidence interval for the mean repair cost in all such vehicle collisions.

The confidence interval is used to test the null hypothesis that the true mean repair cost is $2600. If, in fact, the true mean repair cost is $2600, what would your statistical decision be? Note: We haven't covered confidence interval for means, but the same duality principles and error definition exist.

Reject the null, the p-value must be less than a significance level of 0.01.

Fail to reject the null, the p-value must be less than a significance level of 0.01.

Fail to reject the null, the p-value must be more than a significance level of 0.01.

Reject the null, the p-value must be more than a significance level of 0.01.

2. In the previous question, if the decision made was an error, what type of error was it? Type I , Type II, Type III, or Power

Explanation / Answer

we are given that the 99% confidence interval is

($1066, $2506)

this means that we are 99% sure that the true mean would lie in the range 1066 and 2506 , there is only 1% chance that the true mean would lie outside this range

null hypothesis that the true mean repair cost is $2600

alternate hypothes is  the true mean repair cost is different from $2600

hence based on the confidence interval we

Reject the null, the p-value must be less than a significance level of 0.01.

Also , we know that

type 1 error is : reject null hypothesis when you should not

type 2 error is : accept null hypothesis when you should not

here we are reject the null hypothesis , and if it were wrong , this is a type 1 error .

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