Question

The U.S. Department of Agriculture claims that the mean consumption of bottled water by a person in the United States is 28.5 gallons per year. A random sample of 100 people in the United States has a mean bottled water consumption of 27.8 gallons per year with a standard deviation of 4.1 gallons. At α = 0.08, can you reject the claim? Please show all work!!

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 28.5

H_a :    28.5

= 27.8

= 28.5

= 4.1

n = 100

Test statistic = z

= ( - ) / / n

= (27.8 - 28.5) / 4.1 / 100

= -1.71

Test statistic = -1.71

P(z < -1.71) = 0.0436

P-value = 2 * 0.0436 = 0.0872

= 0.08

P-value >

Fail to reject the null hypothesis .

Fail to reject the claim .