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## MAT 211 SU Interval Estimate of An Average or Proportion in Daily Life Worksheet

### Question Description

(200-250 words for initial post)

Give an example of an interval estimate of an average or proportion you may use in your daily life. For instance, you may say that you are pretty sure your average commute time is between 25-30 minutes, or you are fairly confident that between 60-65% of the population love dogs. Collect some data to see how well your intuition is working. First, does your sample data meet all assumptions necessary to construct the confidence interval of the type you need? Even if it doesnt, construct and interpret the confidence interval.

(100 words each response to 2 class mates) Here below are 2 classmates discussions, they need 100 words each responses. The response should include the answer to the below question. (I will also attach their discussion questions on word documents so that it’s easier to read)

Collect your own data and find your own confidence interval and compare. If, for example, your point estimate is less than your classmates point estimate, can you be sure or confident that the corresponding parameter is less? Why or why not, and what could you do to try to figure it out? What impact do the bounds of the intervals have?

Classmate discussion #1

The estimate I am going to use is the amount of money I carry every day in my wallet. The data represents the amount of money in my wallet for a period of 25 days.

 Amount (\$) 112 156 192 57 45 153 106 152 49 77 189 250 50 175 129 72 84 185 95 202 206 150 142 145 192

The mean amount of money in my wallet is \$134.6.

The standard deviation of money in my wallet is \$57.53.

First, does your sample data meet all assumptions necessary to construct the confidence interval of the type you need? Yes, my sample data meet all assumptions necessary to construct the confidence interval:

1. The sample size of the data is 25.

2. The sample mean and sample standard deviation is defined.

3. In order to construct a confidence interval, I will choose a 95% Confidence interval.

Even if it doesnt, construct and interpret the confidence interval.

95% Confidence Interval will be:

Z-score corresponding to 95% Confidence interval is 1.96.

Confidence Interval = Sample mean ± z*( Sample standard deviation/ Sample size)

= x? ± z*(?/?n)

= 134.6 ± 1.96 * (57.53/?25)

= 134.6 ± 1.96 * 11.51

= 134.6 ± 22.5525

= ( 134.6 – 22.5525, 134.6 + 22.5525)

= ( 112.0475, 157.1525)

Therefore, 95% confidence interval for the amount of money in my wallet is between \$112.0475 and \$157.1525.

Classmate discussion #2

I wanted to check my average footsteps or how much I am walking daily. On an average I am walking around 50000 steps per week. This helps me in my health and fitness and it also reduces the time I have exercise daily. Based on the following data let us track the confidence interval for my footsteps. So on an average my daily level of walking is around 50000 / 7 = 7100 steps. Let us check this data with 95 percent confidence interval.

Confidence interval for proportion p is given by,

ME = 1.96 ^ (.142(.858) / 50000) = .0031

.142 – .0031 < p < .142 + .0031

.1389 < p < .1451

The above calculation shows my confidence interval as .1389 < p < .1451. As you can I determined this data using my step tracker. In that step tracker we can track our daily steps, monthly steps, yearly steps on an average. But the weekly average is not the same here and it may vary based on my daily level of walking. So s data does not satisfy the conditions of the Central Limit Theorem for proportions. Luckily, randomization tests for experiments do not have any assumptions, so we conduct the test using a randomization test. While obtaining the results for this test, it fairly showed the same output, which ultimately means that the data which we used may not be accurate but is fairly approximate. Since a difference of zero (no change) is not within this interval, it is plausible that there has been no big change in the pattern of my weekly steps. But this is not the same for daily steps. We are 95% confident that on an average my daily level of walking around 7000 steps will be between 0.1389 and .1451 points.

Extra Resources!??

Confidence Intervals

· A Single Population Mean using the Normal Distribution

· A Single Population Mean using the Student t Distribution

· A Population Proportion

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