Question

A recent survey of gasoline prices indicated that the national average was $4.098 per gallon. The Dallas Automobile Club claimed that gasoline in Texas was significantly lower than the national average. A survey covering 10 different suburbs in Dallas found the average price of gasoline to be $3.924 per gallon with a population standard deviation of $0.053. What critical value should be used to test the claim using a= 0.01? A recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. It was felt that breakfasts on the West Coast were higher than $7.58. A sample of 81 business managers on the West Coast had an average breakfast cost of $7.65. At a =0.05, what is the critical value?

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 4.098
Alternative Hypothesis: μ < 4.098

Rejection Region
This is left tailed test, for α = 0.01
Critical value of z is -2.33.
Hence reject H0 if z < -2.33

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (3.924 - 4.098)/(0.053/sqrt(10))
z = -10.38

P-value Approach
P-value = 0
As P-value < 0.01, reject the null hypothesis.

2)

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 7.58
Alternative Hypothesis: μ > 7.58

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (7.65 - 7.58)/(0.42/sqrt(81))
z = 1.5

P-value Approach
P-value = 0.0668
As P-value >= 0.05, fail to reject null hypothesis.