Homework SourseTwo major computer companies manufacture and sell computer a
Two major computer companies manufacture and sell computer accessories. The prices of 5 randomly selected accessories are listed below:
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 or cheaper than Pear Computer products
Ha: Macrohard accessories are more expensive
You may find this Student\'s t distribution table useful in answering the following questions. 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 justifiednot justified given the results of the hypothesis test.
| Computer Accessory Price Data | ||
|---|---|---|
| Computer Accessory | Macrohard Price ($) | Pear Computer Price ($) |
| keyboard | 67.95 | 61.81 |
| mouse | 47.54 | 45.13 |
| speaker | 135.39 | 114.3 |
| modem | 122.79 | 94.41 |
| monitor | 376.28 | 355.52 |
Solution
Two major computer companies manufacture and sell computer accessories. The prices of 5 randomly selected accessories are listed below:
Computer Accessory Price Data
Computer Accessory
Macrohard Price ($)
Pear Computer Price ($)
keyboard
67.95
61.81
mouse
47.54
45.13
speaker
135.39
114.3
modem
122.79
94.41
monitor
376.28
355.52
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 or cheaper than Pear Computer products
Ha: Macrohard accessories are more expensive
This is one tailed ( upper tail) test.
You may find this Student\'s t distribution table useful in answering the following questions. 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 = 0.19
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 not justified given the results of the hypothesis test.
Calculated t=0.19
Table value t with 8 Df =1.8595
Calculated t=0.19 < 1.8595 the table value.
The null hypothesis is not rejected.
According to the above data and at a level of significance of 0.05, the claim that Macrohard accessories are more expensive is not justified given the results of the hypothesis test
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
5
Sample Mean
149.99
Sample Standard Deviation
131.7068
Population 2 Sample
Sample Size
5
Sample Mean
134.234
Sample Standard Deviation
126.6250
Intermediate Calculations
Population 1 Sample Degrees of Freedom
4
Population 2 Sample Degrees of Freedom
4
Total Degrees of Freedom
8
Pooled Variance
16690.2870
Standard Error
81.7075
Difference in Sample Means
15.7560
t Test Statistic
0.1928
Upper-Tail Test
Upper Critical Value
1.8595
p-Value
0.4259
Do not reject the null hypothesis
| Computer Accessory Price Data | |||
| Computer Accessory | Macrohard Price ($) | Pear Computer Price ($) | |
| keyboard | 67.95 | 61.81 | |
| mouse | 47.54 | 45.13 | |
| speaker | 135.39 | 114.3 | |
| modem | 122.79 | 94.41 | |
| monitor | 376.28 | 355.52 |
