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 41 27 5 40 30 2 39 30 6 39 34 3 44 35 7 35 29 4 38 30 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 =  d Selectgreater than 10greater than or equal to 10equal to 10less than or equal to 10less than 10not equal to 10Item 1 H a =  d Selectgreater than 10greater than or equal to 10equal to 10less than or equal to 10less than 10not equal to 10Item 2 Calculate the value of the test statistic. If required enter negative values as negative numbers. (to 2 decimals). The p-value is Selectless than .01between .10 and .05between .05 and .10between .10 and .20between .20 and .40greater than .40Item 4 Can you conclude that the price differential is not equal to $10? SelectYesNoItem 5 What is the 95% confidence interval for the difference between the mean prices of the two models (to 2 decimals)? Use a t-table. ( ,  )

any help with this problem would be awesome

Answer 1

Ho: µd is equal to 10

Ha:µd is not equal to 10

S. No	Deluxe	Standard	diff:(d)=x1-x2	d2
1	41	27	14	196.00
2	39	30	9	81.00
3	44	35	9	81.00
4	38	30	8	64.00
5	40	30	10	100.00
6	39	34	5	25.00
7	35	29	6	36.00
	total	=	Σd=61	Σd2=583
	mean dbar=	d̅     =	8.7143
	degree of freedom =n-1                            =		6
	Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) =		2.927700
	std error=Se=SD/√n=		1.1066
	test statistic            =	(d̅-μd)/Se         =	-1.16

p value

=

0.2894

from excel: tdist(1.162,6,2)

p vaue is between 0.2 and 0.40

b)

for 95% CI; and 6 degree of freedom, value of t=			2.447
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		2.707769
lower confidence limit                     =		6.0065
upper confidence limit                    =		11.4221
from above 95% confidence interval for population mean =(6.01,11.42)