Final answer:
To assess if there's a significant difference between the historical and current mean heights of American adult males, a t-test for the difference of means is utilized. The null hypothesis states no significant change, while the alternative hypothesis proposes a significant change. A comparison of the test statistic to the t-distribution's critical value at the given confidence level determines if the null hypothesis is rejected.
Step-by-step explanation:
To determine if the mean height of American adult males has significantly changed since 1902, a geneticist would typically use a hypothesis test for the difference of means. The original study states that the mean height was 67.0 inches with a standard deviation of 3.5 inches. To compare the 1902 figures with the geneticist's recent sample of 28 American adult males with a mean height of 69.4 inches and standard deviation of 4.0 inches, we could use a t-test for the difference between the sample mean and the historical population mean.
The null hypothesis (H0) is that there is no significant difference between the current sample mean and the historical population mean, while the alternative hypothesis (Ha) suggests that there is a significant difference. To conduct the t-test, we'd calculate the test statistic using the sample mean, the historical mean, the sample standard deviation, and the sample size. Based on the degrees of freedom (n-1) and the chosen significance level, usually 0.05 for a 95% confidence level, we'd compare the test statistic to the critical value from the t-distribution to decide if the null hypothesis can be rejected or not.