Question

QUESTION: Last week I gave a statistic from Wikipedia which listed the average weight of a person in North America was 177.9. I don’t think this value is correct. Use our class data to test my claim. Use α=.05.

CLASS DATA:

the average weight of a person is 165.1

the standard deviation is 36.3

Answer 1

Assuming sample size to be 100 since its not mentioned.

The provided sample mean is \bar X = 165.1Xˉ=165.1 and the sample standard deviation is s=36.3, and the sample size is n = 100n=100.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 177.9

Ha: μ ≠ 177.9

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=0.05, and the critical value for a two-tailed test is

tc​=1.984.

The rejection region for this two-tailed test is R={t:∣t∣>1.984}

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=3.526>tc​=1.984, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0006, and since p=0.0006<0.05, 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 \muμ is different than 177.9, at the 0.05 significance level.

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