A manufacturer produces both a deluxe and a standard model of an automatic sande
ID: 3230567 • Letter: A
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.
Model Price ($) Model Price ($)
Retail Outlet Deluxe Standard Retail Outlet Deluxe Standard
1 40 27 5 40 30
2 39 28 6 39 32
3 43 35 7 36 29
4 38 31
a. 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.
Develop the null and alternative hypotheses.
H0 = d
Ha = d
Calculate the value of the test statistic. If required enter negative values as negative numbers. (to 2 decimals).
The p-value is
Can you conclude that the price differential is not equal to $10?
b. What is the 95% confidence interval for the difference between the mean prices of the two models (to 2 decimals)?
( , )
Explanation / Answer
Paired T-Test and CI: delux, standard
Paired T for delux - standard
N Mean StDev SE Mean
delux 7 39.29 2.14 0.81
standard 7 30.29 2.69 1.02
Difference 7 9.000 2.380 0.900
95% CI for mean difference: (6.798, 11.202)
T-Test of mean difference = 10 (vs 10): T-Value = -1.11 P-Value = 0.309
a. P-value >0.05 we do not reject null hypothesis so we conclude that the price differential is equal to $10
b.95% CI for mean difference: (6.798, 11.202)
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