A sample of 17 states found that the average cigarette tax was 91.06 cents with a...

A sample of 17 states found that the average cigarette tax was 91.06 cents with a standard deviation of 38.37 cents. Find the 90% confidence interval for the cigarette tax in all 50 states. Then find the 95% confidence interval for the cigarette tax in all 50 states. How do the confidence intervals compare?

Expert Solution

t critical value at 0.10 level with 16 df = 1.746

90% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

91.06 - 1.746 * 38.37 / sqrt(17) < < 91.06 +1.746 * 38.37 / sqrt(17)

74.812 < < 107.308

90% CI is ( 74.812 , 107.308 )

t critical value at 0.05 level with 16 df = 2.12

90% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

91.06 - 2.12 * 38.37 / sqrt(17) < < 91.06 + 2.12 * 38.37 / sqrt(17)

71.331 < < 110.789

95% CI is ( 71.331 , 110.789 )

95% confidence interval is wider than 90% confidence interval .

orchestra answered 2 years ago

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