Question

Research has shown that dark chocolate, in moderation, is good for your health. Because of this nutritionists try to include this as part of a healthy diet. A client of one of these nutritionists was interested in establishing the average number of calories of a particular dark chocolate bar which was part of his diet.The label on the wrapper indicated that the number of calories in each bar was 280. He took a sample of 19 of these chocolate bars and found that the average number of calories was 286.7 with a standard deviation of 5. Assume that the number of calories in this dark chocolate bar is normally distributed.

Step 1 of 5: Which are the hypotheses to test whether the mean is larger than it is supposed to be?

Step 2 of 5: At α = 0.05, the critical value for the appropriate set of hypotheses is

Step 3 of 5: The value of the test statistic for the hypothesis is

Step 4 of 5: The p-value for a right-tail test of the hypothesis is

Step 5 of 5: What will be the decision for the test at a significance level of 0.05?

Answer 1

STEP 1

we have to  test whether the mean is larger than it is supposed to be, so it is a right tailed hypothesis

STEP 2

sample size is n = 19

degree of freedom = n-1

= 19-1 = 18

using df(18) and alpha level of 0.05 with t distribution table, we get

t critical value = 1.734

STEP 3

test statistic t=

where xbar = 286.7, s = 5, n= 19 and mu = 280

STEP 4

using t distribution table, check df(18) value in the top row and t statistic value in the column, then select the intersecting cell

we get

p value = 0.000

STEP 5

it is clear that the p value is less than significance level of 0.05, this means that the result is significant and we can reject the null hypothesis

therefore, we can say that there is sufficient evidence to conclude that the mean is larger than it is supposed to be