In: Statistics and Probability
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?
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 .