Question

An investigator wants to assess whether the mean μ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 20 passengers showed an average total weight of 195 pounds with a sample standard deviation of 30 pounds. Assume that the population is normally distributed. For a significance level of α = 0.05, do we reject the null hypothesis? Which of the following is an appropriate conclusion?

		The results are statistically significant so the average total weight of all passengers appears to be greater than 185 pounds.
		The results are statistically significant so the average total weight of all passengers appears to be less than185 pounds.
		The results are not statistically significant so there is not enough evidence to conclude the average totalweight of all passengers is greater than 185 pounds.

Answer 1

Given

Hypothesis :

H₀: = 185

H_a: > 185

Test statistic

t = x_bar - /(s/n)

= 185, n =20, x_bar = 195, s = 30

t = (195-185)/(30/20)

t = 1.49

Df = n-1 = 20-1 = 19

Now the p value for t test statistic with 19 degrees of freedom is given by

P value = 0.0763

Conclusion:

The p value (0.0763) is greater than 0.05 hence do not reject null hypothesis at 5% level of significance. It is conclude that the result are not statistically significant so there is not enough evidence to conclude the average total weight of all passengers is greater than 185 pounds.