Question

5 A data set lists earthquake depths. The summary statistics are n = 600, ¯ x = 4.66 km, s = 4.42 km.Usea0.01significanceleveltotesttheclaimof a seismologist that these earthquakes are from a population with a mean equal to 4.00. Assume that a simple random sample has been selected.

Answer 1

The provided sample mean is and the sample standard deviation is s=4.42, and the sample size is n=600.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:

Ha:

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the critical value for a two-tailed test is tc​=2.584.

The rejection region for this two-tailed test is R={t:∣t∣>2.584}

(3) Test Statistics

The t-statistic is computed as follows:

(4) The decision about the null hypothesis

Since it is observed that ∣t∣=3.658>tc​=2.584, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0003, and since p=0.0003<0.01, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is different than 4, at the 0.01 significance level.

Graphically

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