Question

The owner of a gasoline station wants to study gasoline purchasing habits by motorists at his station.  A random sample of 60 motorists during a certain week is selected with the following results

• Amount purchased: mean = 11.3 gallons, standard deviation = 3.1 gallons
• 11 motorists purchased premium grade gasoline

At the 0.05 level of significance, is there evidence that the average purchase in the population is different from 10 gallons?

1. Specify the hypothesis.
2. Compute the test statistic.
3. Find the p-value.
4. What is your conclusion?

Answer 1

Answer:

a)

Given,

Null hypothesis Ho : u = 10

Alternative hypothesis Ha : u != 10

Mean = 11.3

Standard deviation = 3.1

sample n = 60

b)

consider,

test statistic t = (x -u)/(s/sqrt(n))

substitute values

= (10 - 11.3)/(3.1/sqrt(60))

t = -3.25

degree of freedom = n - 1

= 60 - 1

= 59

Here alpha = 0.05

critical value t(alpha/2 , df) = t(0.05/2 , 59) = 2.000995 = +/- 2.001

c)

P value = 0.000521 [since from z table]

d)

Here we observe that, test statistic |t| > critical value, so we reject Ho.

So there is enough evidence.