Question

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.

Answer 1

Give an example of an interval estimate of an average or proportion you may use in your daily life.

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)

= x̄ ± z*(σ/√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.