Olestra is a fat substitute approved by the FDA for use in snack foods. Because

Question

Olestra is a fat substitute approved by the FDA for use in snack foods. Because there have been anecdotal reports of gastrointestinal problems associated with olestra consumption, a randomized, double-blind, placebo-controlled experiment was carried out to compare olestra potato chips to regular potato chips with respect to GI symptoms. Among 523 individuals in the TG control group, 16.6%experienced an adverse GI event, whereas among the 563 individuals in the olestra treatment group, 13.8% experienced such an event.

(a)

Carry out a test of hypotheses at the 5% significance level to decide whether the incidence rate of GI problems for those who consume olestra chips according to the experimental regimen differs from the incidence rate for the TG control treatment. (Use p1 for the TG control group and p2 for the Olestra treatment group.)

State the relevant hypotheses.

H0: p1 p2 = 0
Ha: p1 p2 < 0H0: p1 p2 > 0
Ha: p1 p2 = 0    H0: p1 p2 = 0
Ha: 1 2 > 0H0: p1 p2 < 0
Ha: p1 p2 = 0H0: p1 p2 = 0
Ha: p1 p2 0

Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z=

P-value=

State the conclusion in the problem context.

Fail to reject H0. The data do not suggest a statistically significant difference between the incidence rates of GI problems between the two groups.

Reject H0. The data do not suggest a statistically significant difference between the incidence rates of GI problems between the two groups.  

   Fail to reject H0. The data suggest a statistically significant difference between the incidence rates of GI problems between the two groups.

Reject H0. The data suggest a statistically significant difference between the incidence rates of GI problems between the two groups.

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 0

Hypothesis test results:

Hence,

H0: p1 p2 = 0
Ha: p1 p2 0

z = 1.29

p - Value = 0.1984

Fail to reject H0. The data do not suggest a statistically significant difference between the incidence rates of GI problems between the two groups. Option A

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 86.818 523 77.694 563 0.028 0.021773271 1.2859804 0.1984

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