Question

A magazine collects data each year on the price of a hamburger in a certain fast food restaurant in various countries around the world. The price of this hamburger for a sample of restaurants in Europe in January resulted in the following hamburger prices (after conversion to U.S. dollars).

5.14	4.95	4.07	4.64	5.23	4.67
4.16	4.94	5.15	5.55	5.38	4.60

The mean price of this hamburger in the U.S. in January was $4.62. For purposes of this exercise, assume it is reasonable to regard the sample as representative of these European restaurants. Does the sample provide convincing evidence that the mean January price of this hamburger in Europe is greater than the reported U.S. price? Test the relevant hypotheses using

α = 0.05.

(Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

State your conclusion.

Reject H₀. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.62.Do not reject H₀. We do not have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.62.    Do not reject H₀. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.62.Reject H₀. We do not have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.62.

Answer 1

here we use t test for single sample as the sample size n= 12

Hypothesis

Null hypothesis : The mean January price of hamburger in Europe is equal to the reported U.S.

Alternative Hypothesis : The mean January price of hamburger in Europe is greater than the reported U.S.

using microsoft excel command datas -> data analysis -> t test for two samples assuming unequal variances

we get the output as below

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1
Mean	4.873333333
Variance	0.211315152
Observations	12
Hypothesized Mean Difference	0
df	11
t Stat	36.72412206
P(T<=t) one-tail	3.67824E-13
t Critical one-tail	1.795884819
P(T<=t) two-tail	7.35647E-13
t Critical two-tail	2.20098516

here aplha = 0.05,

t value = 36.72

p value = 0.000

here p value =0.000 < 0.05

we reject Ho at aplha = 0.05

i.e we accept H1

The mean January price of hamburger in Europe is greater than the reported U.S.

Conclusion :  Reject H₀. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.62