A manufacturer produces both a deluxe and a standard model of an automatic sande
ID: 3156934 • 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. 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. H_0 = mu_d equalto 10 H_a = mu_d not equal to 10 Calculate the value of the test statistic. If required enter negative values as negative numbers, (to 2 decimals). -1.99 The p-value is between .20 and.40 Can you conclude that the price differential is not equal to $10? No What is the 95% confidence interval for the difference between the mean prices of the two models (to 2 decimals)?Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: ud = 10
Ha: ud =/ 10
At level of significance = 0.05
As we can see, this is a two tailed test.
The differences are
14
9
9
8
10
5
6
Calculating the standard deviation of the differences (third column):
s = 4.981024599
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 1.882650338
Calculating the mean of the differences (third column):
XD = 8.714285714
As t = [XD - uD]/sD, where uD = the hypothesized difference = 10 , then
t = -0.682927817 [ANSWER, TEST STATISTIC]
***********************************************
For the 0.95 confidence level,
alpha/2 = (1 - confidence level)/2 = 0.025
t(alpha/2) = 2.446911851
lower bound = [X1 - X2] - t(alpha/2) * sD = 4.107606291
upper bound = [X1 - X2] + t(alpha/2) * sD = 13.32096514
Thus, the confidence interval is
( 4.107606291 , 13.32096514 ) [ANSWER]
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