Question

Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds:

125  147  240  186  156  205  248  152  199  207  176

Phil also completes a simple random sample of non-professional athletes and records his results in pounds:

151  161  139  128  149  160  201  173

The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same.

1) What population parameter is being tested? (mean, proportion etc)
2) How many populations are being tested?
3) Calculate the sample mean weight of professional athletes (round to the nearest ten-thousandth).
4) What is the claim? (At this point, you should have already selected the formula that will be used to calculate the test statistic and written it in the test statistic box.) What is the alternative hypothesis?
5) What is the test statistic (rounded to the nearest thousandth)?
6) The critical region is best described as (right/left/2)
7) What is the largest lower bound of the p-value from the table (rounded to the nearest hundredth) or the value of the p-value found using technology (rounded to the nearest ten-thousandth?)
8) What is the significance level (expressed as a decimal)?
9) What is the statistical conclusion?

Answer 1

1) What population parameter is being tested? (mean, proportion etc)

Answer : Here we are testing the parameter mean.
2) How many populations are being tested?

Answer : Here we are testing 2 populations
3) Calculate the sample mean weight of professional athletes (round to the nearest ten-thousandth).

Answer : Sample mean weight of professional atheletes = 185.5455

sample standard deviation = s₁ = 45.22

Sample mean weight of non-professional atheletes = 157.75

sample standard deviation = s₂ = 22.2889

4) What is the claim? (At this point, you should have already selected the formula that will be used to calculate the test statistic and written it in the test statistic box.) What is the alternative hypothesis?

Answer : Here the alternative Hypothesis is mean weights of of professional and non-professional athletes are the differet
5) What is the test statistic (rounded to the nearest thousandth)?

Here pooled standard deviation = s_p = [{(n₁ -1)s₁² + (n₂ -1)s₂²}/(n₁ + n₂ -2)]

s_p = 37.5154

standard erroro of proportion = sqrt [s_p * (1/n₁+ 1/n₂)] = 17.432

Test statitic

t = (185.5455 - 157.75)/17.432 = 1.5945

6) The critical region is best described as (right/left/2)

Here critical region is two tailed. where alpha = 0.02 and dF = 11 + 8 -2 = 17

t_critical= 2.567

7) What is the largest lower bound of the p-value from the table (rounded to the nearest hundredth) or the value of the p-value found using technology (rounded to the nearest ten-thousandth?)

Here p - value is in between from the table is 0.1292 and in between 0.1 and 0.2
8) What is the significance level (expressed as a decimal)?

Here significance level = 0.02 or 98%
9) What is the statistical conclusion?

Here as p - values > 0.02 so we failed to reject null hypothesis and conclude that there is no difference in mean weights of professional and non-professional athletes.