High School

A random sample of 150 women and 150 men from the California Health Survey were selected, and the following results were obtained:

- Among the 150 women, the mean age is 59.6 years, and the standard deviation is 17.7 years.
- Among the 150 men, the mean age is 59.1 years, and the standard deviation is 16.9 years.

Using a 0.05 significance level, is there sufficient evidence to support the claim that the mean age of an adult California woman is the same as the mean age of an adult California man?

Answer :

Final answer:

To determine if the mean age of women is the same as the mean age of men, we can perform a two-sample t-test.

Explanation:

To determine if there is sufficient evidence to support the claim that the mean age of an adult California woman is the same as the mean age of an adult California man, we can perform a two-sample t-test.

The null hypothesis is that the mean age of women is the same as the mean age of men, and the alternative hypothesis is that the mean age of women is different from the mean age of men.

We can calculate the t-statistic using the formula:

t = (mean1 - mean2) / sqrt((sd1^2 / n1) + (sd2^2 / n2))

Where mean1 and mean2 are the sample means, sd1 and sd2 are the sample standard deviations, and n1 and n2 are the sample sizes.

If the absolute value of the t-statistic is greater than the critical value (obtained from a t-distribution table or using software), we can reject the null hypothesis and conclude that there is sufficient evidence to support the claim.

Learn more about Two-sample t-test here:

https://brainly.com/question/32606144

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