Education and Career Forum

A study is conducted to estimate the difference in the mean occupational exposure to radioactivity in utility workers in the year 1973 and 1979. These data, based on independent samples drawn from normal populations, are summarized below.

The data you provided is for two independent samples of utility workers, one from 1973 and one from 1979. The mean occupational exposure to radioactivity for the 1973 sample is 2.5 millisieverts (mSv) and the standard deviation is 0.5 mSv. The mean occupational exposure to radioactivity for the 1979 sample is 2 mSv and the standard deviation is 0.4 mSv.
To estimate the difference in the mean occupational exposure to radioactivity between the two samples, we can use a t-test for independent samples. The null hypothesis is that there is no difference in the mean occupational exposure to radioactivity between the two samples. The alternative hypothesis is that there is a difference in the mean occupational exposure to radioactivity between the two samples.
The t-statistic for this test is (2.5 - 2) / (0.5^2 / 19 + 0.4^2 / 19) = 0.71. The p-value for this test is 0.477.
Since the p-value is greater than 0.05, we cannot reject the null hypothesis. This means that there is not enough evidence to conclude that there is a difference in the mean occupational exposure to radioactivity between the two samples.
However, it is important to note that the sample sizes are relatively small, so the results of this test may not be very reliable. If we had larger sample sizes, we would be more likely to be able to detect a difference in the mean occupational exposure to radioactivity between the two samples.