A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population.
A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately
| Subject | Cholestrol Level (mg/dl) | Cholestrol Level after 6 Weeks (mg/dl) | dd | ¯dd¯ | (d−¯d)2(d-d¯)2 |
|---|---|---|---|---|---|
| 1 | 206 | 217 | 11 | ||
| 2 | 219 | 184 | -35 | ||
| 3 | 202 | 204 | 2 | ||
| 4 | 213 | 205 | -8 | ||
| Total | -30 |
a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer:
- ¯d=d¯= (do not round)
- ∑(d−¯d)2=∑(d-d¯)2= (do not round)
- sd=sd= (rounded to one decimal place)
b) Perform the hypothesis test in the following steps:
Step 1. State the null and alternative hypotheses by selecting the appropriate symbol:
H0:H0:
H1:H1:
Step 2. Find the critical value(s):
- If you use z-table, then state the closest left cumulative area in the table to find the critical value. If you use t-table, then state 1 tail or 2 tails αα value (in decimals) with the degrees of freedom, separated by a comma.
- State the critical value(s): CV=
Step 3. State the rejection region:
- Select from the dropdown menu to shade to the left, to the right, between or left and right of the critical value(s); and then shade the rejection region(s). The arrow can only drag to the critical value(s) that is/are rounded to one decimal place (these values correspond to the tick marks on the horizontal axis). Note: If CV < -4, then use -4.0 and if CV > 4, then use 4.0.
Shade: . Click and drag the arrows to adjust the values.
-1.5 - Reject H0 if test statistic value the critical value(s). (Select >< if outside of two CV or <> if between two CV)
Step 4. Calculate the test statistic: Show your work using the numerical values in the formula and round the answer to 3 decimal places.
test statistic == ==
Step 5. Decision:
Since the test statistic is the critical value(s), we H0H0 at α=α=0.2.
Step 6. Conclusion statement:
- There is not sufficient evidence to conclude that the mean of four subjects' cholesterol levels has been changed after six weeks.
- There is sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks.
- There is not sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks.
- There is sufficient evidence to conclude that the mean of four subjects' cholesterol levels has been changed after six weeks.
Step by step
Solved in 9 steps with 1 images
