Question

Watch your weight: A study published in 2008 reported that the mean weight of men aged 40−59 was 89.3 kg. Another study, published in 2016 , reported that a sample of 198 men aged 40-59 had an average weight of 90.5 kg. Assume the population standard devlation is σ=14.4 kg. Can you conclude that the mean weight of men aged 40−59 is higher in 2016 than in 2008 ? Use the α=0.10 level of significance. Part: 0/5 Part 1 of 5 (a) State the appropriate null and alternate hypotheses. H0​H1​​ The hypothesis tent is a test.

Answer 1

The null hypothesis (H0) is that there has been no increase in the mean weight of men aged 40-59 since 2008, while the alternative hypothesis (H1) states that the mean weight has increased. A one-tailed test will be used with an alpha level of 0.10.

Step-by-step explanation:

To determine whether the mean weight of men aged 40−59 is higher in 2016 compared to 2008, we conduct a hypothesis test using the given data. The null hypothesis (H0) and the alternative hypothesis (H1) are as follows:

H0: μ = 89.3 kg (the mean weight has not increased since 2008)

H1: μ > 89.3 kg (the mean weight has increased since 2008)

This is a one-tailed test since we are interested in whether the mean weight has increased and not just changed. We will use an alpha level of 0.10 to determine the significance of our results.

Given the population standard deviation (σ) is 14.4 kg, the sample size (n) is 198, the sample mean (μ bar) is 90.5 kg, and the alpha level is 0.10, we can calculate the z-score to compare the sample mean to the population mean

Answer 2

The appropriate null and alternate hypotheses are H0 : The mean weight of men aged 40-59 in 2016 is not higher than in 2008, and H1 : The mean weight of men aged 40-59 in 2016 is higher than in 2008. To determine if there is enough evidence to reject the null hypothesis, we need to perform a hypothesis test using a t-test. We would need additional information such as the sample size and the results of the hypothesis test to analyze further.

Step-by-step explanation:

The appropriate null and alternate hypotheses in this case are:

H0: The mean weight of men aged 40-59 in 2016 is not higher than in 2008.

H1: The mean weight of men aged 40-59 in 2016 is higher than in 2008.

To determine if there is enough evidence to reject the null hypothesis, we need to perform a hypothesis test. We will use a one-sample t-test since we have the mean and standard deviation of the population and want to compare the means of two samples.

Here are the steps to perform the hypothesis test:

State the null and alternative hypotheses

Set the significance level (α)

Calculate the test statistic

Determine the critical value(s)

Compare the test statistic to the critical value(s)

Draw a conclusion and state the results

Since the significance level is given as α=0.10, we will set α=0.10 in this test. Based on the sample means and assuming a normal distribution, we can calculate a t-score using the formula:
t = (sample mean - population mean) / (population standard deviation / √sample size)

Once we calculate the t-score, we can compare it to the critical value(s) from the t-distribution table to determine if it falls in the critical region. If it does, we reject the null hypothesis. If it doesn't, we fail to reject the null hypothesis.

However, we need additional information in order to perform the actual calculations, such as the sample size and the results of the hypothesis test.