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

1. 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 10
   H _a = _d Selectgreater than 10greater than or equal to 10equal to 10less than or equal to 10less than 10not equal to 10
   
   Calculate the value of the test statistic. If required enter negative values as negative numbers. Use z-table. (to 2 decimals).
   
   
   The p-value is Selectless than .01between .10 and .05between .05 and .10between .10 and .20between .20 and .40greater than .40
   
   Can you conclude that the price differential is not equal to $10?
   SelectYesNo
   
2. What is the 95% confidence interval for the difference between the mean prices of the two models (to 2 decimals)?
   ( , )

Answer 1

After performing 2 sample t test for the data in MINITAB, the results are given below:

the hypotheses are given in the above output.

the value of test statistic is -0.77.

the p-value is 0.456. (Greater than 0.4). do not reject the null hypothesis.

NO,

it cannot be concluded as the difference is not equal to $10.

the 95% confidence interval for the difference in the means is (6.1700, 11.8300)