Question

It is believed that the mean flight time from Seattle to New York City is 310 minutes. You want to test to determine if it is different from this. The population standard deviation is 10 minutes. You randomly sample 50 flights and the sample average is 313 minutes.

State your hypotheses, calculate and state the test statistic, calculate and state the p-value, state whether you reject the Ho or fail to reject the Ho, and state your final conclusion (i.e. sufficient or insufficient evidence ...).

Answer 1

(i)

H0: Null Hypothesis: = 310 ( the mean flight time from Seattle to New York City is 310 minutes)

HA: Alternative Hypothesis: 310 ( the mean flight time from Seattle to New York City is different from 310 minutes) (Claim)

(ii)

SE = /

= 10/

= 1.4142

Test Statistic is given by:

Z = (313 - 310)/1.4142

= 2.1213

The test statistic is 2.1213

(iii)

By Technology, Cumulative Area Under Standard Normal Curve = 0.9831

So,

p - value = (1 - 0.9831) X 2 = 0.0338

(iv)

Take = 0.05

Since p - value = 0.0338 is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:
There is sufficient evidence to support the claim that the mean flight time from Seattle to New York City is different from 310 minutes.