In Exercises 1–10, based on the nature of the given data, do t...

Question

In Exercises 1–10, based on the nature of the given data, do the following:

a. Pose a key question that is relevant to the given data.

b. Identify a procedure or tool from this chapter or the preceding chapters to address the key question from part (a).

c. Analyze the data and state a conclusion.

Video Games In a survey of subjects aged 18–29, subjects were asked if they play video games often or sometimes. Among 1017 males, 72% answered “yes.” Among 984 females, 49% answered “yes” (based on data from a Pew Research Center survey).

Accepted Answer

In a recent survey of adults aged 30 to 45, participants were asked if they regularly consume energy drinks. Out of 850 men, 38% responded yes. Out of 920 women, 25% responded yes. So our tasks are to pose a key question relevant to this data. Identify an appropriate statistical procedure or tool to address the question. And analyze the data and state a conclusion. Now, the question I posed is, is there a significant difference between the women and men aged from 30 to 45, who regularly consume energy drinks? So now we need our statistical procedure. In this case, we will use. A 2 proportion. Z. Since we have two proportions. We can use this test. So let's note down what we have. We have our sample of men, with the sample size, being 850. And the proportion Being 0.38. For women The sample size, It's 920. And the proportion is 0.25. Now, let's find the number of successes first. In this case, A number of successes for men will be 850, multiplied by 0.38. Which is 323. For women This will be 0.25, multiplied by 920. Which gives us 230. Now that we have these values, let's calculate our pooled proportion, PA. This is given by X1 + X2, divided by N1 plus N2. In this case, we have 323. Plus 230, divided by 850 plus 920. Which approximately gives us 0.3124. Now, let's find the standard error. Standard error is given by the square root of Phat multiplied by 1 minus Phat. Multiplied by 1 divided by N1 plus 1 divided by N2. This is 0.3124, multiplied by 1 minus 0.3124. Multiply it again by 1 divided by 850, plus 1 divided by 920. We can simplify this. It ends up. Getting our standard error to be 0.02205. Now, we will use this to find our Z score. R Z Will be our difference in proportions. P 1 minus P2. Divided by our standard error. In this case, We have 0.38 minus 0.25 divided by 0.02205. This simplifies to be 5.90. Now this Z is a large Z value. If our Z value is large enough, we can then assume that we will reject our hypothesis and claim our alternative. We can then say That this is statistically significant. We can then claim that there is a difference between men and women with energy drink consumption. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

Key Concepts

Descriptive Statistics

Hypothesis Testing

Data Analysis Techniques

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