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Answer :
To determine if the mean weight of males is less than 150 pounds, a one-sample t-test is used. The decision to reject the null hypothesis is based on comparing the calculated t-statistic to the critical value from a t-distribution table for the given significance level and degrees of freedom.
To determine the final decision for the claim that the mean weight of males is less than 150 pounds, we can use a one-sample t-test assuming that the population standard deviation is not known and the sample size is smaller than 30. If the population standard deviation were known or the sample size were large, we would use a z-test instead. However, in this case, we are given a sample of 41 individuals with a sample mean of 145 pounds and a standard deviation of 16 pounds.
The hypothesis being tested (null hypothesis, H0) is that the mean weight is ">= 150 pounds". The alternative hypothesis (Ha) is that the mean weight is "< 150 pounds". For a significance level (">") of 0.05, we would reject the null hypothesis if the calculated t-statistic falls into the rejection region, which would be the left tail of the t-distribution corresponding to a critical t-value. The t-statistic is calculated as follows:
t = (sample mean - population mean) / (s/√n) = (145 - 150) / (16/√41)
After calculating this value, you would compare it to the critical t-value from the t-distribution table for 40 degrees of freedom (n-1) at the 0.05 significance level. If the t-statistic is less than the critical t-value, you reject H0. If it is greater, you fail to reject H0.
The decision would be based on comparing the calculated t-statistic with the critical t-value. If a < p-value, as stated in a similar example, you do not reject H0.
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