Question

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

0.01

significance level. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, and conclusion for the test. Assume this is a simple random sample.

Magnitude of Earthquake   

0.720

0.740

0.640

0.390

0.700

2.200

1.980

0.640

1.220

0.200

1.640

1.320

2.950

0.900

1.760

1.010

1.260

0.000

0.650

1.460

1.620

1.830

0.990

1.560

0.410

1.280

0.830

1.350

0.540

1.250

0.920

1.000

0.790

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

1. What are the​ hypotheses?

2. Determine the test statistic.

3.Determine the​ P-value.

4. State the final conclusion that addresses the original claim

Answer 1

Let u denotes the population mean. Hypotheses : To test null hypothesis Ho := 1 against alternative hypothesis H : > 1 Let 7 denotes the sample mean, s denotes the sample standard deviation and n denotes the sample size. Here, J = 1.185, 82 = 0.344299, s = 0.59, n = 50 The test statistic can be written as: m(z - 1) t= S which under Ho follows a t distribution with n-1 df. Decision rule / Rejection region : We reject H, at 0.05 level of significance if P-value < 0.05 or if tobs > t0.05,n-1 = 1.676551 0.4- 0.3- 0.2 0.1 0.0 - -2 Now, Value of the test statistic: The value of the test statistic tobs V50 (1.1850 - 1) 0.5868 = 2.229404 2.23 associated degrees of freedom = 49 The critical value tcritical = t0.05, n-1 = t0.05,49 = 1.676551 1.68 P-value = P(t 49 > 2.229404) =1- P(t49 <2.229404) = 1-0.984798 = 0.015202 0.0152 Conclusion : Since p-value < 0.05 and tobs > tcritical = 1.676551, so we reject H, at 0.05 level of significance Hence, we can conclude that population mean is significantly greater than 1