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. Develop the null and alternative hypotheses.

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)?

Model Price ($) Model Price ($) Retail Outlet Deluxe Standard Retail Outlet Deluxe Standard 1 39 27 5 40 30 2 39 28 6 39 34 3 45 35 7 35 29 4 38 30

Explanation / Answer

Below are the null and alternate hypothesis

H0: mu1 - mu2 = 10

H1: mu1 - mu2 not equals to 10

p-value = 0.4880

As p-value is greater than the significance level of 0.05, we fail to reject null hypothesis. This means there is not sufficient evidence that price differential is not equal to $10.

(b)

For 95% CI, t-value = 2.1788

lower limit = (mu1 - mu2) - t*SE = 8.8571 - 2.1788*1.6 = 5.3772

upper limit = (mu1 - mu2) + t*SE = 8.8571 + 2.1788*1.6 = 12.3371

Given Data Sample 1 Sample 2 Name Deluxe Standard mean 39.2857 30.4286 Sample size 7 7 Std. dev. 2.98 2.99

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