2. A sample of 25 American women who are between 19 and 30 years old, found that

Question

2. A sample of 25 American women who are between 19 and 30 years old, found that they consumed a mean of 1791 calories per day with a standard deviation of 13 calories per day. At the 10% level of significance, can we show that the mean calorie consumption of all American women between the ages of 19 and 30 is not 1750 calories?

(a) State and test appropriate hypotheses. State Conclusions.

(b) If an error was made in (a) what type of error was it?

(c) What assumption is needed for the analysis in (a) to be appropriate?

Explanation / Answer

Solution:

a. Null Hypothesis (Ho): µ = 1750

Alternative Hypothesis (Ha): µ 1750

Test Statistics

t = (X-bar - µ)/ (s/n)

t = (1791 – 1750)/ (13/25)

t = 15.77

Degrees of freedom, df = n – 1 = 25 – 1 = 24

Using t-tables, the critical value at a = 0.10/2 = 0.05 and df = 24 is

t (0.05, 24) = 1.711

Since test statistics is greater than the critical value, we reject the null hypothesis.

Hence, we can conclude that the mean calorie consumption of all American women between the ages of 19 and 30 is not 1750 calories.

b. It is a type 1 error of rejecting the null hypothesis when it is true.

c. The assumption is that it is normally distributed.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.