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Answer :
Using the appropriate inference test, we can conclude that there is evidence to support the researcher's belief that men weigh more today than in previous years.
To determine if there is a significant difference in the weights of men between the present and previous years, we can conduct a hypothesis test. Since the researcher believes that men weigh more today, this is a one-tailed test.
The null hypothesis, denoted as H0, states that the mean weight of adult men is equal to the previous mean weight of 181 lbs. The alternative hypothesis, denoted as Ha, states that the mean weight of adult men is greater than 181 lbs.
Using the given sample of 41 adult men, we can calculate the test statistic using the formula:
Z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
Substituting the given values, we obtain:
Z = (198 - 181) / (11.2 / sqrt(41)) ≈ 3.59
Next, we compare the test statistic to the critical value at the desired significance level (e.g., α = 0.05). If the test statistic exceeds the critical value, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.
Looking up the critical value in the standardized normal distribution table or using statistical software, we find that the critical value for a one-tailed test at α = 0.05 is approximately 1.645.
Since the calculated test statistic of 3.59 exceeds the critical value of 1.645, we reject the null hypothesis. Therefore, we conclude that there is evidence to support the researcher's belief that men weigh more today than in previous years based on the provided sample.
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