Question

The data table below contains the amounts that a sample of nine customers spent for lunch​ (in dollars) at a​ fast-food restaurant

4.23 5.08 5.96 6.45 7.43 7.54 8.36 8.51 9.76

a) At the 0.05level of​ significance, is there evidence that the mean amount spent for lunch is different from ​$6.50​?

b) Calculate test stastics ( four decimals places)

C) Calculate P value and explain interpretations ( four decimal places)?

d) Because the sample size is​ 9, do you need to be concerned about the shape of the population distribution when conducting the t test in​? Explain.

Answer 1

b) Here the test statistic is

Here = 7.0355

= specified population mean which we want to test. = 6.50

s = Standard deviation f data = 1.7662

n = 9

Therefor test statistic value is 0.9096

C) p-value is .3896

• p-value is lowest possible value of level of significance at which we can reject our null hypothesis.
• As a rule of thumb if the p-value is less than our level of significance then we reject the null hypothesis

a) Since the p-value is greater than 0.05, we reject the claim that the mean amount spent for lunch is different from ​$6.50​ .

d) t-test can be used for small samples also.

NOTE : There are other assumptions which have to be satisfied for t-test but sample size is not a constraint.