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.

0.720, 0,740, 0.640, .390, .700, 2.200, 1.980, .640, 1.220, .200, 1.640, 1.320, 2.950, .900, 1.760, 1.010, 1.260, 0.000, .650, 1.460, 1.620, 1.830, .990, 1.560, .390, 1.280, .830, 1.350, .540, 1.250, .920, 1.000, .780, .790, 1.440, 1.000, 2.240, 2.500, 1.790, 1.250, 1.490, .840, 1.000, 1.250, 1.420, 1.350, .930, .400, 1.390

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.

a. Identify the test statistic. (Round to two decimal places as needed.)

b. Identify the P-value. (Round to three decimal places as needed.)

Answer 1

Since the problem is to test whether the population of earthquakes has a mean magnitude greater than 1.00, we use One sample t-test to test this claim.

GIVEN:

Sample size ​ (as only 49 magnitudes are given).

To find sample mean, I used excel function "=AVERAGE(select array of 49 magnitude values)"

Sample mean

To find sample standard deviation, I used excel function "=STDEV(select array of 49 magnitude values)".

Sample standard deviation

HYPOTHESIS:

The hypothesis for one sample t test is given by,

​ (That is, the population of earthquakes has a mean magnitude greater than or equal to 1.00).

​ (That is, the population of earthquakes has a mean magnitude less than 1.00).

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

which follows t-distribution with ​ degrees of freedom.

where is sample mean.

​ is the hypothesized value 1.00.

​ is sample standard deviation.

is sample size.

CALCULATION:

CRITICAL VALUE:

The left-tailed (since ​) t critical value with ​ degrees of freedom at significance level ​ is .

DECISION RULE:

.

INFERENCE:

Since the calculated t statistic value (2.13) is greater than the t critical value (-2.407), we fail to reject ​ and conclude that the population of earthquakes has a mean magnitude greater than or equal to 1.00.

P VALUE:

The corresponding p-value for t statistic value 2.13 with 48 degrees of freedom is ​. (In the 48 degrees of freedom row, check for the p-value which has nearest t-statistic value.)

INFERENCE:

Since the calculated p-value is which is greater than the significance level , we fail to reject ​ and conclude that the population of earthquakes has a mean magnitude greater than or equal to 1.00.