Question

An advertisement for a popular supermarket chain claims that it has had consistently lower prices than four other full-service supermarkets. As part of a survey conducted by an "independent market basket price-checking company," the average weekly total, based on the prices (in $) of approximately 95 items, is given for two different supermarket chains recorded during 4 consecutive weeks in a particular month.

Week	Advertiser ($)	Competitor ($)
1	254.21	256.02
2	240.63	255.65
3	231.99	255.20
4	234.22	261.08

(a) Is there a significant difference in the average prices for these two different supermarket chains? (Use α = 0.05. Round your answers to three decimal places.)

1-2. Null and alternative hypotheses:

H₀: μ_d < 0 versus H_a: μ_d > 0

H₀: μ_d = 0 versus H_a: μ_d ≠ 0    

H₀: μ_d ≠ 0 versus H_a: μ_d = 0

H₀: μ_d = 0 versus H_a: μ_d < 0

H₀: μ_d = 0 versus H_a: μ_d > 0

3. Test statistic:  t =  

4. Rejection region: If the test is one-tailed, enter NONE for the unused region.

t >

t <

5. Conclusion:

H₀ is rejected. There is sufficient evidence to indicate that the means are different.

H₀ is not rejected. There is insufficient evidence to indicate that the means are different.    

H₀ is not rejected. There is sufficient evidence to indicate that the means are different.

H₀ is rejected. There is insufficient evidence to indicate that the means are different.

(b) What is the approximate p-value for the test conducted in part (a)?

p-value < 0.010

0.010 < p-value < 0.020    

0.020 < p-value < 0.050

0.050 < p-value < 0.100

0.100 < p-value < 0.200

p-value > 0.200

(c) Construct a 99% confidence interval for the difference in the average prices for the two supermarket chains. (Round your answers to two decimal places.)
$  to $  

Interpret this interval.

Since 0 falls in the confidence interval, there is sufficient evidence to indicate that the means are different.

Since 0 does not fall in the confidence interval, there is sufficient evidence to indicate that the means are different.    

Since 0 does not fall in the confidence interval, there is insufficient evidence to indicate that the means are different.

Since 0 falls in the confidence interval, there is insufficient evidence to indicate that the means are different.

Answer 1

a)H0: μd = 0 versus Ha: μd ≠ 0

3)

Test statistic:  t = -3.011

4)

t >3.182

t<-3.182

5

H0 is not rejected. There is insufficient evidence to indicate that the means are different.   

b)

0.050 < p-value < 0.100

c)

for 99% CI; and 3 degree of freedom, value of t=
therefore confidence interval=		sample mean -/+ t*std error
margin of errror          =t*std error=		32.440
lower confidence limit                     =		-49.16
upper confidence limit                    =		15.71

-49.16 to 16.71

Since 0 falls in the confidence interval, there is insufficient evidence to indicate that the means are different.