Question 4 [5 points]
A news website believes that equal to 42% of its visitors click on advertisements while on the site. A sample of size 48 visitors is taken and it is observed that 25 of them clicked on ads. Perform a
hypothesis test to test the null hypothesis that equal to 42% of website visitors click ads against the alternative hypothesis,
H1, that something other than 42% click on ads, with level of significance α = 0.02.
| a) | What type of test would be appropriate in this situation? | A right-tailed test. | | A left-tailed test. | | A two-tailed test | | None of the above. |
|
b) What is the computed
p-value?
For full marks your answer should be accurate to at least three decimal places.
p-value: 0
| c) | Based on your p-value and the decision rule you have decided upon, what can we conclude about H0? | There is sufficient evidence, at the given significance level, to reject H0. | | There is insufficient evidence, at the given significance level, to reject H0; or we fail to reject H0. | | There is insufficient evidence to make it clear as to whether we should reject or not reject the null hypothesis |
|
Question 5 [8 points]
A large online store prides itself on its fast response to email questions to its technical department. Listed below is the time, in hours, that the technical department took to respond to 17 sample emails.
| 58.44 | 50.58 | 53.28 | 44.64 | 56.40 | 54.60 | 59.34 | 59.34 | 57.48 | 56.76 | 54.78 | 63.48 |
| 51.30 | 40.44 | 46.56 | 47.52 | 56.58 |
The store has recently hired more staff members, and wants to know if the time to respond to emails has dropped from last year's average of 55.49 hours. At the 0.05 significance level, is it reasonable to conclude the average response time is less than last year's average? Follow the steps below to answer this question.
| a) | Select the null and alternative hypotheses. | H0: μ < 55.49
H1: μ ≥ 55.49 | | H0: μ = 55.49
H1: μ ≠ 55.49 | | H0: μ ≥ 55.49
H1: μ < 55.49 |
|
| b) | We will use the t-statistic for this question, but is there another way? If any, what assumptions must we make? | No, there is no other way in this instance, but we have to assume the population is normal. | | No, there is no other way in this instance, and we don't have to make any assumptions. | | Yes, there is another way. We could choose to use the z-statistic because of the results of the central limit theorem. |
|
c) Compute the
p-value. For full marks, your answer should be accurate to three decimal places.
p-value: 0
| d) | Draw your conclusion for this one-sample test. | Do not reject H0. | | Reject H0 and accept H1. | | We do not have enough information to decide. |
|
Question 9 [5 points]
Given that the null hypothesis and alternative hypothesis are:
H0: The categories are equal. H1: The categories are not equal.
| Category | f0 |
|---|
| | A | 30 | | B | 10 | | C | 10 | | D | 30 | | E | 20 | | F | 40 | | G | 20 | | H | 10 |
|
| a) | Using a 0.01 significance level, what is the decision rule? | Reject H0 if X2 > 18.475. | | Reject H0 if X2 > 20.3. | | Reject H0 if X2 > 16.622. | | Reject H0 if X2 < 18.475. |
|
b) Compute the value of the Chi-Square.
For full marks your answer should be accurate to at least two decimal places.
Chi-Square: 0
| c) | State the decision regarding H0. | Reject H0. | | Do not Reject H0. | | Can not be determined based on our results. |
|