Holiday Toys manufactures and distributes its products through more than 1,000 r

Question

Holiday Toys manufactures and distributes its products through more than 1,000 retail outlets. For this year's most important new toy, Holiday's marketing director is expecting demand to average (40) units per retail outlet. Assuming the population is normally distributed, a sample of (25) retailers provided a mean of (37.4) units with a standard deviation of (11.79) units.

At the .05 level of significance, is the population mean quantity per retail outlet different from (40) units? (Show All Work)

Explanation / Answer

Data:    

n = 25   

= 40   

s = 11.79   

x-bar = 37.4   

Hypotheses:   

Ho: = 40   

Ha: 40   

Decision Rule:   

= 0.05   

Degrees of freedom = 25 - 1 = 24

Lower Critical t- score = -2.063898547

Upper Critical t- score = 2.063898547

Reject Ho if |t| > 2.063898547

Test Statistic:   

SE = s/n = 11.79/25 = 2.358

t = (x-bar - )/SE = (37.4 - 40)/2.358 = -1.10263

p- value = 0.281122641   

Decision (in terms of the hypotheses):

Since 1.102629347 < 2.063899 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that the population mean quantity per retail outlet is different from 40.

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