Q3. An important hypothesis in hypertension research is that sodium restriction may lower blood pressure. However, it is difficult to achieve sodium restriction over the long term, and dietary counseling in a group setting is sometimes used to achieve this goal. The data on urinary sodium in HW4 Q3.sav on Canvas were obtained from 8 individuals enrolled in a sodium-restricted group. Data were collected at baseline and after 1 week of dietary counseling. Assume the population of urinary sodium follows a normal distribution.

1. What are appropriate hypotheses to test whether dietary counseling is effective in reducing sodium intake over a 1-week period (as measured by overnight urinary sodium excretion)? Explain why.

2. Carry out the test procedure mentioned in part 1). Use = 0.05, and both rejection region and p-value to make a decision.

3. Provide a 95% CI for the true mean change in overnight sodium excretion over a 1-week period. Interpret the confidence interval.

Data given:

Person, week 0, week 1, difference

1 7.85 9.59 -1.74 2 12.03 34.50 -22.47 3 21.84 4.55 17.29 4 13.94 20.78 -6.84 5 16.68 11.69 4.99 6 41.78 32.51 9.27 7 14.97 5.46 9.51 8 12.07 12.95 -.88