Question

15. The accompanying data table lists the magnitudes of 50 earthquakes measured on the Richter scale. Test the claim that the population of earthquakes has a mean magnitude greater than 1.00. Use a 0.05 significance level. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, and conclusion for the test. Assume this is a simple random sample.

0.690

0.740

0.640

0.390

0.700

2.200

1.980

0.640

1.220

0.200

1.640

1.330

2.950

0.900

1.760

1.010

1.260

0.000

0.650

1.460

1.620

1.830

0.990

1.560

0.390

1.280

0.830

1.340

0.540

1.250

0.920

1.000

0.780

0.790

1.440

1.000

2.240

2.500

1.790

1.250

1.490

0.840

1.420

1.000

1.250

1.420

1.350

0.930

0.400

1.390

Identify the test statistic.____

(Round to three decimal places as​ needed.)

Identify the critical​ value(s).____

(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

Identify the​ P-value.

The​ P-value is ____

​(Round to four decimal places as​ needed.)

Answer 1

n = 50

sample mean =

standard deviation = S =0.588

claim : The population of earthquakes has a mean magnitude greater than 1.00

Null and alternative hypothesis is

Level of significance = 0.05

Here population standard deviation is not known so we use t-test statistic.

Test statistic is

Degrees of freedom = n - 1 = 50-1=49

critical value =1.677 ( using t table)

P-value = 0.0158 ( using t table)

P-value , Reject H0

conclusion : At level of significance ,there is sufficient evidence to conclude that the population of earthquakes has a mean magnitude greater than 1.00