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meaQuestion
1
1.
The table below summarises the results of a survey of online computer gamers, which included questions on the type of network connection used (dial-up, ADSL or cable) and the performance level of the respondent’s hardware (classified as low, medium, high or extreme). (Note: very few respondents indicated low hardware performance, so this group was combined with the “medium” group.)
net connection \ hardware
low/medium
high
extreme
Total
dial-up
9
5
15
ADSL
17
22
10
49
cable
5
10
6
21
31
37
17
85
To carry out a statistical test to assess whether there is any evidence of a relationship between hardware performance and connection type, what is the null hypothesis?
Answer
|
Hardware Performance and Connection type are dependent |
|
Hardware Performance and Connection type are independent |
|
The mean Hardware Performance for all Connection Types are equal |
|
The mean Hardware Performance for all Connection Types are not equal |
1 points
Question 2
1.
What is the expected number of ADSL users with computers in the extreme category?
Answer
1.5 points
Question 3
1.
Given that the expected number of cable users with computers in the low/medium category is 7.66, calculate the corresponding term in the test statistic?
Answer
1.5 points
Question 4
1.
Which distribution tables should be used when looking up the test statistic for this test (including the degrees of freedom, if relevant)?
Answer
|
Chi-Squared tables with 4 degrees of freedom |
|
Chi-Squared tables with 3 degrees of freedom |
|
Chi-Squared tables with 2 degrees of freedom |
|
Standard Normal table with 4 degrees of freedom |
1.5 points
Question 5
1.
If the p-value for the test is determined to be approximately 0.214, what conclusion would you draw?
Answer
|
There is strong evidence that hardware performance is dependent on connection type |
|
There is slight evidence that hardware performance is independent of connection type. |
|
There is insufficient evidence that hardware performance is dependent on connection type. |
|
There is not enough information given to enable a conclusion to be drawn. |
1 points
Question 6
1.
A claim has been made that an ADSL user is twice as likely to be using hardware in the high category than in the extreme category but equally likely to be using hardware in the low/medium or high categories. A statistical test is to be carried out to assess this claim. What is the null hypothesis for this test?
Answer
|
For ADSL users, an equal proportion use low/medium, high hardware and extreme hardware. |
|
For ADSL users, 40% use low/medium hardware, 20% use high hardware and 40% use extreme hardware. |
|
For ADSL users, 20% use low/medium hardware, 40% use high hardware and 40% use extreme hardware. |
|
For ADSL users, 40% use low/medium hardware, 40% use high hardware and 20% use extreme hardware. |
1 points
Question 7
1.
For the test of Question 6, calculate the expected number of ADSL users with hardware in the high category
Answer
1 points
Question 8
1.
Which distribution tables should be used when looking up the test statistic for this test from Question 6 (including the degrees of freedom, if relevant)?
Answer
|
Ch-Squared tables with 4 degrees of freedom. |
|
Ch-Squared tables with 3 degrees of freedom. |
|
Ch-Squared tables with 2 degrees of freedom. |
|
Standard Normal tables with 4 degrees of freedom. |
1 points
Question 9
1.
The p-value for this test is 0.725. From this, we can say that …
Answer
|
There is insufficient evidence to suggest that the proportions of ADSL users using low/medium, high and extreme hardware are different from the given proportions. |
|
There is some evidence to suggest that the proportions of ADSL users using low/medium, high and extreme hardware are different from the given proportions. |
|
There is strong evidence to suggest that the proportions of ADSL users using low/medium, high and extreme hardware are different from the given proportions. |
|
There is insufficient evidence to suggest that the proportions of ADSL users using low/medium, high and extreme hardware are the same. |
1.5 points
Question 10
1.
Another test was carried out to assess the claim that cable users were equally likely to use hardware in any of the three categories. The test statistic for this test was 2.00. Determine the approximate p-value for this test, showing briefly how it is obtained from the relevant table.
Answer
1.5 points
Question 11
1.
Based on the above data, an approximate 95% confidence interval for the proportion of cable users who have hardware in the low/medium category is given by What is the value of n?
Answer
1 points
Question 12
1.
What is the value of c from Question 11?
Answer
1 points
Question 13
1.
It is claimed that a cable user is more likely to use extreme hardware than an ADSL user. In testing this claim, what is the null hypothesis? Note p1 is the proportion of cable users who use extreme hardware and p2 is the proportion of ADSL users who use extreme hardware
Answer
|
H0 : p1 does not equal p2 |
|
H0 : p1 < p2 |
|
H0 : p1 > p2 |
|
H0 : p1 = p2 |
1 points
Question 14
1.
What is the alternative hypothesis for the test in Question 13?
Answer
|
H1 : p1 does not equal p2 |
|
H1 : p1 < p2 |
|
H1 : p1 > p2 |
|
H1 : p1 = p2 |
1 points
Question 15
1.
The test statistic for this test is given by What is the value of p1_hat?
Answer
1 points
Question 16
1.
What is the value of p2_hat in Question 15?
Answer
1 points
Question 17
1.
What is the value of m in Question 15?
Answer
0.5 points
Question 18
1.
What is the value of n in Question 15?
Answer
0.5 points
Question 19
1.
What is the value of p-hat in Question 15?
Answer
1 points
Question 20
1.
Based on the above data, the test statistic is 0.744. Determine the (approximate) p-value for the test?
Answer
