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Given the oft-cited statistic that 66.7% of the American public is overweight or obese, you are interested in comparing college students BMI level to the general population.

Assuming that the general population has a BMI of (μ) = 27.5 using α level of .05, you hypothesize that college students will have a lower BMI than the general population.

State the null and alternative hypothesis and the critical value. Conduct a single-sample t-test based on the following data. Provide an approximate p-value and your conclusion.

Also, what would be the critical value if this was a two-tailed test and what would be your conclusion regarding reject/fail to reject the null hypothesis?

Given this, provide a 95% confidence interval (for the single sample t-test we’ll do the CI around the sample mean, though you can also do it around the difference between the sample mean and population mean).

Further, what shape does the distribution of scores take? What is your conclusion?


BMI

24.00
28.00
22.00
28.00
24.00
21.00
23.00
32.00
25.00
23.00
22.00
21.00
30.00
21.00
22.00

  • statistics -

    You'll need to calculate the mean and standard deviation. Both of these values will be needed in the following formula:
    t = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

    Ho: µ = 27.5 -->null hypothesis
    Ha: µ < 27.5 -->alternative hypothesis

    Use a t-table at 0.05 level of significance for a one-tailed test (alternative hypothesis shows a specific direction) at 14 degrees of freedom (df = n - 1 = 15 - 1 = 14).

    Once you have the critical value from the table, compare the test statistic to the critical value after you finish the calculations from the formula. If the test statistic exceeds the critical value from the table, reject the null. If the test statistic does not exceed the critical value from the table, do not reject the null. Do the same for a two-tailed test. Remember to check the t-table for two-tailed to obtain the correct critical values (there will be a plus and minus value since this will be two-tailed). To find the p-value, use the table again. The p-value is the actual level of the test statistic.
    To find the 95% confidence interval around the sample mean, use the critical values from the two-tailed test in the appropriate confidence interval formula. Draw your conclusions from the results you find.

    I hope these few hints will help get you started.

  • statistics -

    This helps a LOT. Thank you very much for your time.

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