The quality of the computer accessories for both companies are practically the s
ID: 3334670 • Letter: T
Question
The quality of the computer accessories for both companies are practically the same because both companies purchase the parts from the same wholesaler. Since the market for these accessories is very competitive, the main reason why one product would be more expensive than another would be due to brand name and the advertizing related to it.
A computer periodical claims that Macrohard products are generally more expensive than Pear Computer products. You plan to do a hypothesis test on this claim where:
H0: Macrohard accessories are equal in price to Pear Computer products
Ha: Macrohard accessories are more expensive
You may assume that the differences in prices are normally distributed.
a)Calculate the test statistic (t) that is best suited in conducting this hypothesis test. Give your answer to 2 decimal places.
t =
b)According to the above data and at a level of significance of 0.05, the claim that Macrohard accessories are more expensive is justified or not justified given the results of the hypothesis test.
Computer Accessory Price Data Computer Accessory Macrohard Price ($) Pear Computer Price ($) keyboard 48.22 50.7 mouse 56.60 48.71 speaker 160.38 162.38 modem 104.62 97.01 monitor 456.51 366.45Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Macrohard - Pear< 0
Alternative hypothesis: Macrohard - Pear > 0
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).
s = sqrt [ ((di - d)2 / (n - 1) ]
s = 39.36
SE = s / sqrt(n)
S.E = 2.806
DF = n - 1 = 5 -1
D.F = 4
t = [ (x1 - x2) - D ] / SE
t = 7.205
where di is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 4 degrees of freedom is more extreme than 7.205; that is, less than - 7.205 or greater than 7.205
Thus, the P-value = 0.001
Interpret results. Since the P-value (0.001) is less than the significance level (0.05), we have to reject the null hypothesis.
b) According to the above data and at a level of significance of 0.05, the claim that Macrohard accessories are more expensive is justified.
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