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A random sample of 17 size AA batteries for toys yield a mean of 3.89 hours with standard deviation, 0.63 hours.

(a) Find the critical value, t*, for a 99% CI. t* =

User Dumi Jay
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Final answer:

To find the critical value, t*, for constructing a 99% confidence interval for a sample size of 17, one must refer to a t-distribution table or use statistical software, considering the degrees of freedom (n-1) and the area in the tails.

Step-by-step explanation:

The student's question is asking for the critical value t* for constructing a 99% confidence interval for a sample mean based on a sample of 17 size AA batteries. To find this t critical value (t*), we must refer to a t-distribution table or use statistical software since the sample size is small (n < 30) and we assume the underlying distribution of the population is normally distributed.

To find t*, we look for the t-value that corresponds to the area in the tails (1-confidence level) for a 99% confidence interval with degrees of freedom (df) = n - 1, where n is the sample size. In this case, df = 17 - 1 = 16. The critical value t* will be the value when the area in both tails is 0.5% (since it's 99% CI), making it a one-tailed distribution of 0.995. Consulting a t-distribution table or using software will provide us with the critical value.

User Urvish
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