Hypothesis Testing: Internet Usage for a Company
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1. Choose two test statistics and describe how they are used.
2. Using the author's data set, perform the following two hypothesis tests on statements from the author.
Perform a hypothesis test to examine this statement by the author: "The average internet usage for a country in 2017 is 60%."
● Write a null hypothesis and alternate hypothesis.
● Interpret type 1 and type 2 errors for the null hypothesis.
● Using alpha = .05, and a t distribution, graph the rejection region.
● Conclude whether to reject or not to reject the null hypothesis.
● Does your statistical analysis support the author's statement?
Perform a hypothesis test to examine this statement by the author: "Surprisingly internet usage is not as high as most think—only 50% of countries had widespread internet usage in 2017 (widespread internet usage is defined as 75% or more of a population using the internet)."
● Write a null hypothesis and alternate hypothesis.
● Interpret any type 1 and type 2 errors for the null hypothesis.
● Using alpha = .01, and a normal distribution, graph the rejection region.
● Conclude whether to reject or not to reject the null hypothesis.
● Does your statistical analysis support the author's statement?
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Solution Summary
Step-by-steps explanations are given in the Word file. All formulas used are shown. The Excel file contains further details of formulas and calculations.
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1. Choose two test statistics and describe how they are used.
The following are 2 tests statistics:
A z test statistic is used in hypothesis testing when the population standard deviation is known and the sample size is large (n > 30). In hypothesis testing, the null and alternative hypotheses are first stated. Then the data are used to calculate the z test statistic. The z test statistic is then used to find the p-value which is in turn compared to the significance level.
In a hypothesis test where the population mean is tested against a value, the z test statistic is calculated in the following manner:
(see the attachment for the full visual solution)
where
A t test statistic is used in hypothesis testing when the population standard deviation is unknown and the sample size is small (n≤30). In hypothesis testing, the null and alternative hypotheses are first stated. Then the data are used to calculate the t test statistic. The t test statistic is then used to find the p-value which is in turn compared to the significance level.
where
s = sample standard deviation
n = ...
Education
- MSc, California State Polytechnic University, Pomona
- MBA, University of California, Riverside
- BSc, California State Polytechnic University, Pomona
- BSc, California State Polytechnic University, Pomona
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