Question

For all questions: (a) state the null and alternative hypotheses, (b) conduct appropriate statistical methods with alpha-.05, (c) report your final statistics with a decision regarding the null hypothesis, and (d) summarize your results in your own words. 1. In this era of credit cards there is discussion on whether or not coin use is declining. A professor has been collecting data for years on the number of cents people carry in their pockets or purses and maintains that the population mean is 2.2 cents. She polls her current class and obtains the following data: 1, 2, 3, 0, 0, 19, 43, 2, 7, 9, 0, 0, 1, 0, 5. Has there been a change in the number of cents people carry? (Report the appropriate statistics and state whether you reject or accept the null hypothesis)

Answer 1

(1)

Data:    

n = 15   

μ = 2.2   

s = 11.40092   

x-bar = 6.13333   

Hypotheses:   

Ho: μ = 2.2   

Ha: μ ≠ 2.2   

Decision Rule:   

α = 0.05   

Degrees of freedom = 15 - 1 = 14

Lower Critical t- score = -2.144786681

Upper Critical t- score = 2.144786681

Reject Ho if |t| > 2.144786681

Test Statistic:   

SE = s/√n = 11.40092/√15 = 2.943704886

t = (x-bar - μ)/SE = (6.13333 - 2.2)/2.9437048860962 = 1.336184

p- value = 0.202802752   

Decision (in terms of the hypotheses):

Since 1.336183535 < 2.144787 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that there is a change in the number of cents people carry.