Question

For a recent year, the mean fare to fly from Charlotte, North Carolina to Chicago Illinois, on a discount ticket was $290. A random sample of 12 round trip discount fares on this route last month shows:

286

290

285

291

287

275

262

289

274

276

297

262

At the 0.01 significance level, can we conclude that the mean fare has decreased? What is the p value?

1. State the Null and Alternate hypothesis:
2. State the test statistic:
3. State the Decision Rule:
4. Show the calculation:
5. What is the interpretation of the sample data?
6. Show the P value

Answer 1

it's a left-tailed test

from the given data, we get

n = 12

test statistic:

= -2.70

df = n-1 = 11

critical value, tc = -2.718 (from t-table)

decision rule: reject Ho if t < -2.718

here, t > -2.718, we fail to reject Ho

there is not enough evidence to conclude that  the mean fare has decreased.

p-value = 0.0103 (from t-table)

upvote if it helps, thank you.