A manufacturer produces both a deluxe and a standard model of an automatic sande

Question

A manufacturer produces both a deluxe and a standard model of an automatic sander designed for home use. Selling prices obtained from a sample of retail outlets follow.

The manufacturer's suggested retail prices for the two models show a $10 price differential. Use a .05 level of significance and test that the mean difference between the prices of the two models is $10.

a) Calculate the value of the test statistic. If required enter negative values as negative numbers. (to 2 decimals).


b) The p-value is .......
Can you conclude that the price differential is not equal to $10?

c) What is the 95% confidence interval for the difference between the mean prices of the two models (to 2 decimals)? ( step by step please)
( ,  )

Model Price ($) Model Price ($) Retail Outlet Deluxe Standard Retail Outlet Deluxe Standard 1 39 27 5 40 30 2 39 29 6 39 35 3 46 35 7 35 29 4 38 31

Explanation / Answer

from above applying matched paired t test:

as p value is higher then 0.05 level we can not conclude that the price differential isequal to $10

for 95% CI and 6 degree of freedom t =2.4469

hence 95% confidence interval =sample mean -/+ t*std error =5.86 ; 11.29

deluxe standard difference(d) 39 27 12 39 29 10 46 35 11 38 31 7 40 30 10 39 35 4 35 29 6 mean 8.571 std deviaition 2.9358 std error= std dev/(n)^(1/2) 1.1096 t stat= (d-10)/std error -1.2874 p value = 0.1194

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