Question

opose the data shown here are the results of a survey to investigate gas prices. Ten service stations were randomly selected in each city and the figures represent the prices of a litre of unleaded regular gas. What can we tell about the relative price of gas in the two cities? Calgary Edmonton 1.029 0.999 1.02 1.026 1.017 1.017 1.002 1.008 0.996 0.99 1.017 1.038 1.014 1.017 1.014 1.032 1.014 1.011 0.983 1.014 Design a test to determine if there is a difference in mean gas prices in the two cities use alpha -,01 Quiz #8 Generate a 95% confidence interval estimate for the true mean difference in gas prices in the 2 cities. Does this interval confirm the results from your test above?

Answer 1

In order to solve this question I used R software.

R codes and output:

> d=read.table('gas.csv',header=TRUE, sep=',')
> head(d)
calgary edmonton
1 1.029 0.999
2 1.020 1.026
3 1.017 1.017
4 1.002 1.008
5 0.996 0.990
6 1.017 1.038
> attach(d)
> var(calgary)
[1] 0.0001769333
> var(edmonton)
[1] 0.0002104
> t.test(calgary,edmonton,var.equal=TRUE)

Two Sample t-test

data: calgary and edmonton
t = -0.73912, df = 18, p-value = 0.4694
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.017675321 0.008475321
sample estimates:
mean of x mean of y
1.0106 1.0152

Hypothesis:

Hopi = pz

217 In: H

Since we don't know population standard deviation we use t test. Both the sample have approximately equal variances. Hence we use t test with equal variances.

Test statistic ,

t =  -0.73912, with df = 18,

p-value = 0.4694

P-value is greater than 0.05, hence we accept null hypothesis and conclude that there is no significant difference between mean gas price in the two cities.

Que.8

95% confidence interval for mean difference = (-0.017675321, 0.008475321)

Since confidence interval contain zero, we accept null hypothesis.