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Hypothesis Testing with Z-Test

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Hypothesis test for the difference of population means: Z test
According to the historical data, the life expectancy in the United States is equal to the life expectancy in the United Kingdom. A new study has been made to see whether this has changed. Records of 200 individuals from the United States who died recently are selected at random. The 200 individuals lived an average of 76.7 years with a standard deviation of 5.1 years. Records of 300 individuals from the United Kingdom who died recently are selected at random and independently. The 300 individuals lived an average of 77.5 years with a standard deviation of 5.4 years. Assume that the population standard deviation of the life expectancy can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the life expectancy,u1 , in the United States is not equal to the life expectancy,u2 , in the United Kingdom anymore? Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Write the formula for: The null hypothesis

Write the formula for: The alternative hypothesis

Type of test statistic? Z, T, Chi square or f.

The p value. Round at least 3 decimals.

Can we support the claim that the life expectancy in the United States is not equal to life expectancy in the United Kingdom? Yes or No

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Solution Summary

This solution provides the null and alternative and calculates the z-test statistic to compare to the calculated p-value. It then makes a decision to either accept or reject the null hypothesis.

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