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

PLEASE SHOW ALL STEPS AND WORK

Answer 1

Solution:

x	x2
286	81796
290	84100
285	81225
291	84681
28	784
275	75625
262	68644
289	83521
274	75076
276	76176
297	88209
262	68644
∑x=3115	∑x2=868481

Mean ˉx=∑xn

=286+290+285+291+28+275+262+289+274+276+297+262/12

=3115/12

=259.5833

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√868481-(3115)212/11

=√868481-808602.0833/11

=√59878.9167/11

=√5443.5379

=73.7803

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :    = 290

H_a : < 290

Test statistic = t

= ( - ) / S / n

= (259.58 - 290) / 73.78 / 12

= −1.428

Test statistic = t = −1.428

The critical value = −2.718

P-value =0.0905

= 0.01

P-value >

0.0905 > 0.01

Fail to reject the null hypothesis .

There is not sufficient evidence to claim that the population mean μ is less than 290, at the 0.01 significance level.