Question

Adult male height is assumed to be normally distributed with a mean of 175.5 cm within the population. A sample of 26 college students was recruited to have their heights measured, and the mean height was 182 cm, with a standard deviation of 17 cm. Researchers want to know if the collected sample has a height that is significantly different from that of the population mean. Use 2 decimal points for all your calculations. Using a significance level of 0.01, answer the following questions. (a) What type of statistical test should the researchers conduct? Why? (1 mark) (b) State the hypotheses for this scenario. (1 mark) (c) Conduct a hypothesis test based on question 1a) to determine what the researcher should conclude from this study. Write your decision using the critical value method and confidence interval method. Relate it to the research question. (2 marks)

          Adult male height is assumed to be normally distributed with a mean of 175.5 cm within the population. A sample of 26 college students was recruited to have their heights measured, and the mean height was 182 cm, with a standard deviation of 17 cm. Researchers want to know if the collected sample has a height that is significantly different from that of the population mean. Use 2 decimal points for all your calculations. Using a significance level of 0.01, answer the following questions.

(a) What type of statistical test should the researchers conduct? Why? (1 mark)
(b) State the hypotheses for this scenario. (1 mark)
(c) Conduct a hypothesis test based on question 1a) to determine what the researcher should conclude from this study. Write your decision using the critical value method and confidence interval method. Relate it to the research question. (2 marks)

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Added by Austin C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Steve Galvin

06/09/2022

Step 1

- The researchers should conduct a one sample T test because they are comparing the sample mean to a known population mean. Show more…

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Adult male height is assumed to be normally distributed with a mean of 175.5 cm within the population. A sample of 26 college students was recruited to have their heights measured, and the mean height was 182 cm, with a standard deviation of 17 cm. Researchers want to know if the collected sample has a height that is significantly different from that of the population mean. Use 2 decimal points for all your calculations. Using a significance level of 0.01, answer the following questions. (a) What type of statistical test should the researchers conduct? Why? (1 mark) (b) State the hypotheses for this scenario. (1 mark) (c) Conduct a hypothesis test based on question 1a) to determine what the researcher should conclude from this study. Write your decision using the critical value method and confidence interval method. Relate it to the research question. (2 marks)

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00:01 Okay, so the answer to part a is you should definitely conduct a one -sample t test because this is the test that you use when you're comparing a sample mean to a claimed mean.

00:12 T -tests are usually for significance tests about population means.

00:18 Part b, state your hypotheses.

00:21 Well, since the claim is that the average should be 175 .5, then the null hypothesis should be mu equals 175 .5.

00:35 Now, it says that they want to find out if the sample is significantly different to that of the population mean.

00:46 So since it doesn't say significantly higher or significantly lower, it says significantly different, you say mu is not equal to 175 .5 for your alternative hypothesis.

01:01 Okay.

01:03 Now we want to run the test for part c.

01:06 You were given that the mean of the sample is 182.

01:10 You need to calculate the standard error of the sample mean, the standard error of x bar, which is given by the formula, the standard deviation of the sample, which is 17 divided by the square root of the sample size, and it says 26 college students were used.

01:33 So we're going to divide 17 by the square of 26.

01:38 17 divided by the square of 26 is 3 .33.

01:47 Okay.

01:48 So the standard error is 3 .33.

01:51 All right.

01:53 So now you've got to calculate your t score, your t value, your critical value, which you do by taking the mean of your sample minus what the mean of the sample was expected to be, which was 175 .5, divided by 3 .33.

02:12 So we're going to grab our calculator, 182 minus 175 .5 divided by 3 .33...

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