# 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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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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