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Video Games: Checking Requirements Twelve different video games showing alcohol use were observed. The duration times of alcohol use were recorded, with the times (seconds) listed below (based on data from 鈥渃ontent and rating of Teen-Rated Video Games,鈥 by Haninger and Thompson, journal of the American Medical Association, Vol.291, No.7). What requirements must be satisfied to test the claim that the sample is from a population with a mean greater than 90 sec? Are the requirements all satisfied?

84 14 583 50 0 57 207 43 178 0 2 57

Short Answer

Expert verified

The requirements for the given data are the sample should be selected randomly, and the data should be normally distributed (or sample size must be larger than 30).

All the requirements do not satisfy.

Step by step solution

01

Given information

The duration times of alcohol use for 12 different video games were recorded. The population mean=90sec.

02

State the hypotheses

For the true mean value , the hypothesis is stated as follows:

H0:=90(nullhypothesis)H1:>90(alternativehypothesisandoriginalclaim)

03

State the requirements

The following requirements need to be verified for conducting the test:

  1. The given sample is selected randomly from the population.
  2. The sample size is either larger than 30 or the population is distributed normally.
04

Check the requirements

The normal Q-Q plot is sketched using the following steps:

  1. Draw two axes, horizontal and vertical.
  2. Mark z-scores corresponding to the observations on the change by means of scaling the axes.
  3. Thus, the relevant graph along with a tentative line is shown below.

The points are not close to the straight line; they deviate. Hence, this is not normally distributed.

Also, the sample is not specified to be selected by random selection.

Thus, the requirements are not satisfied.

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Most popular questions from this chapter

Using Confidence Intervals to Test Hypotheseswhen analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.

a.Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

b.Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

c.Use the sample data to construct a 95% confidence interval estimate of the proportion of zeros. What does the confidence interval suggest about the claim that the proportion of zeros equals 0.1?

d.Compare the results from the critical value method, the P-value method, and the confidence interval method. Do they all lead to the same conclusion?

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Requirements and Conclusions

a. Are any of the three requirements violated? Can the methods of this section be used to test the claim?

b. It was stated that we can easily remember how to interpret P-values with this: 鈥淚f the P is low, the null must go.鈥 What does this mean?

c. Another memory trick commonly used is this: 鈥淚f the P is high, the null will fly.鈥 Given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how is this memory trick misleading?

d. Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like 0.0483?

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