Question

A researcher is conducting a study on numbers of Facebook users. Suppose Facebook reports that, based on user data from the provided 32 countries, the mean number of Facebook users is about 24,000,000 per country. Use a t-test in Minitab to determine whether or not the data provided yields a statistically significant result. A. Go to Stat->Basic Statistics->1-Sample t… and after selecting the proper variable, perform a hypothesis test with a hypothesized mean equivalent to what Facebook reports. Make sure you remember to go into options and choose the 2-tailed test option.

Descriptive Statistics

N   Mean   StDev   SE Mean   95% CI for μ
32   61270496   105721785   18689148   (23153727, 99387264)
μ: mean of Internet Users

Test

Null hypothesis   H₀: μ = 24000000
Alternative hypothesis   H₁: μ ≠ 24000000
T-Value   P-Value
1.99   0.055

What is the resulting p-value?

B. Is this a statistically significant result?

C. Repeat the process, but this time assume that Facebook tells the researcher there are 35,000,000 users per country (mean).

Test

Null hypothesis   H₀: μ = 35000000
Alternative hypothesis   H₁: μ ≠ 35000000
T-Value   P-Value
1.41   0.170

What is the resulting p-value?

D. Is part C’s p-value indicative of a statistically significant result? E. What conclusion should the researcher publish based on your results from parts C and D?

Answer 1

To test,

Null hypothesis, H₀: μ = 24000000 (not statistically significant)
Alternative hypothesis , H₁: μ ≠ 24000000 (statistically significant)

A.) For the user data with mean 24000000, the p- value is 0.055

B.) To test the statistical significance, the decision rule is, if p-value > , we accept the null hypothesis, we reject otherwise.

Here, we assume significance level () to be 0.05

Since, p-value > 0.05, we accept the null hypothesis at 5% significance level.

Therefore, this is not statistically significant. at 5% level of significance.

Further, to test,

Null hypothesis, H₀: μ = 35000000  (not statistically significant)
Alternative hypothesis, H₁: μ ≠ 35000000 (statistically significant)

C.) Here, p-value = 0.170

D.) We have, p-value > 0.05, hence, we accept  H₀ at 5% significance level.

Conclusion: At 5% significance level, the data provided do not yield a statistically significant result.

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