Final answer:
A one-sample t-test can be used to test the hypothesis that the mean weights of the population is greater than 60 kg. The test statistic is calculated as (sample mean - population mean) / (sample standard deviation / sqrt(sample size)), and compared to the critical value for a one-tailed test at a 0.01 level of significance. In this case, the test statistic is -7.07 and the critical value is -2.33, leading us to reject the null hypothesis and support the alternative hypothesis.
Step-by-step explanation:
To test the hypothesis that the mean weights of the population is greater than 60 kg, we can use a one-sample t-test.
The null hypothesis (H0) is that the mean weight of the population is 60 kg, and the alternative hypothesis (Ha) is that the mean weight is greater than 60 kg.
The test statistic can be calculated as:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
In this case, the test statistic is t = (58 - 60) / (4 / sqrt(200)) = -2 / (4 / sqrt(200)) = -2 / 0.283 = -7.07 (rounded to two decimal places).
Since this is a one-tailed test and our alternative hypothesis is that the mean weight is greater than 60 kg, we can compare the test statistic to the critical value for a one-tailed test at a 0.01 level of significance.
The critical value for a one-tailed test at a 0.01 level of significance is approximately 2.33.
Since the test statistic (-7.07) is less than the critical value (-2.33), we reject the null hypothesis. There is strong evidence to support the alternative hypothesis that the mean weights of the population is greater than 60 kg.