Critical value: z = 2.33. Fail to reject null hypothesis. There is not sufficient evidence to support the claim
that more than half of all those using the drug experience relief.
-Find the P-value for a test to support the claim that less than 50% of the people following a particular diet will experience increased energy. Of 100 randomly selected subjects who followed the diet, 47 noticed an increase in
Their energy level.
A) 0.2743
B) 0.5486
C) 0.2257
D) 0.7257

Question

Quizplus · Accepted Answer

We can use a one-tailed hypothesis test with the null hypothesis being that the proportion of people who experience increased energy is 0.5 or higher, and the alternative hypothesis being that the proportion is less than 0.5.

We can use the formula: 
z = (p̂ - p) / sqrt(p*(1-p)/n)
where p̂ is the sample proportion, p is the hypothesized population proportion, n is the sample size, and sqrt stands for square root.

Plugging in the values, we get: 
z = (0.47 - 0.5) / sqrt(0.5*(1-0.5)/100) 
z = -0.75

Using a standard normal table or calculator, we can find the p-value associated with this z-score to be 0.2743. This means that if the true proportion of people who experience increased energy is actually 0.5 or higher, there is a 27.43% chance of observing a sample proportion of 0.47 or lower.

Since this p-value is greater than the typical significance level of 0.05, we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that less than 50% of the people following the diet will experience increased energy.

Critical Value: Z = 2