Webcredible, a UK-based consulting firm specializ- ing in websites, intranets, mobile devices, and applications, conducted a survey of 1,132 mobile phone users between February and April 2009. The survey found that 52% of mo- bile phone users are now using the mobile Internet. (Data extracted from “Email and Social Networking Most Popular Mobile Internet Activities. The authors of the article imply that the survey proves that more than half of all mobile phone users are now using the mobile Internet.
a. Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to try to prove that more than half of all mobile phone users are now using the mo- bile Internet.
b. Based on your result in (a), is the claim implied by the authors valid?
c. Suppose the survey found that 53% of mobile phone users are now using the mobile Internet. Repeat parts (a) and (b).
d. Compare the results of (b) and (c).
You can try a proportional one-sample z-test for this one since this problem is using proportions.
Null hypothesis:
p ≤ .50
Alternate hypothesis:
p > .50
Using a formula for a proportional one-sample z-test with your data included, we have:
z = .52 - .50 -->test value minus population value
divided by
√[(.50)(.50)/1132]
Finish the calculation. Determine the p-value using the z-score you calculate. (The p-value is the actual level of the test statistic.) Compare to the level of significance for a one-tailed test, which is 0.05. Determine whether or not to reject the null and conclude a difference (p > .50). For part c, redo the same process using .53 instead of .52.
(Hint: One null hypothesis will be rejected; one will not.)
I hope this will help get you started.
a. To test whether more than half of all mobile phone users are now using the mobile Internet, we can use the five-step p-value approach to hypothesis testing.
Step 1: Formulate the null hypothesis (H0) and the alternative hypothesis (Ha):
- Null hypothesis (H0): Less than or equal to 50% of mobile phone users are using the mobile Internet.
- Alternative hypothesis (Ha): More than 50% of mobile phone users are using the mobile Internet.
Step 2: Determine the level of significance (α):
- The level of significance is given as 0.05.
Step 3: Collect the data and perform the statistical test:
- Given that the survey found that 52% of mobile phone users are now using the mobile Internet, we can perform a one-sample proportion hypothesis test.
Step 4: Calculate the test statistic and p-value:
- Using a statistical software or calculator, calculate the test statistic and p-value for the given data. The test statistic is typically the z-score for proportions.
Step 5: Make a decision:
- If the p-value is less than the level of significance (0.05), we reject the null hypothesis in favor of the alternative hypothesis. This would suggest that more than half of all mobile phone users are using the mobile Internet.
b. Based on the result obtained in part (a), if the p-value is less than 0.05, we can conclude that the claim implied by the authors is valid. This means that there is evidence to support the statement that more than half of all mobile phone users are using the mobile Internet.
c. Suppose the survey found that 53% of mobile phone users are now using the mobile Internet. We can repeat the five-step p-value approach to hypothesis testing using the new data.
- Null hypothesis (H0): Less than or equal to 50% of mobile phone users are using the mobile Internet.
- Alternative hypothesis (Ha): More than 50% of mobile phone users are using the mobile Internet.
Repeat steps 2-5 using the new data and perform the hypothesis test. Calculate the test statistic and p-value.
d. Compare the results of parts (b) and (c):
- If the p-value in part (c) is less than 0.05, we reject the null hypothesis and conclude that more than half of all mobile phone users are using the mobile Internet based on the updated survey findings.
- If the p-value in part (c) is greater than 0.05, we fail to reject the null hypothesis and do not have enough evidence to support the claim that more than half of all mobile phone users are using the mobile Internet based on the updated survey findings.
Comparing the results of (b) and (c) will help determine whether the change from 52% to 53% significantly affects the conclusion. If the p-value in part (c) is still less than 0.05, the claim implied by the authors remains valid.