Li keeps track of the time he spends working out each week. The table shows the number of cardio workouts and the number of weig
hted workouts for 3 recent weeks. The total time in minutes for weeks 1 and 2 are given. Each cardio workout is the same length of time, and each weighted workout is the same length of time. The system of equations can be used to represent this situation. Use the drop-down menus to complete each statement.
2 answers:
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Answer:
(a) The point estimate of the proportion of the population who would answer yes is 0.295.
(b) The margin of error for a 95% confidence interval is 0.0259.
(c) 95% confidence interval for population proportion is [0.2691 , 0.3209].
Step-by-step explanation:
We are given that a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the environment, 352 of 1195 subjects said yes.
Let = <u><em>sample proportion of subjects who said yes.</em></u>
(a) The point estimate of the proportion of the population who would answer yes = =
So, = <u>0.295</u>
(b) Margin of error is given by =
where, = level of significance = 1 - 0.95 = 5%
At 5% level of significance, z table gives critical value of 1.96 for two-sided interval.
Standard of error = =
= 0.0132
So, Margin of error for 95% confidence interval =
= <u>0.0259</u>
(c) 95% confidence interval for population proportion is given by =
Point estimate Margin of error
⇒ 0.295 0.0259
⇒ [0.295 - 0.0259 , 0.295 + 0.0259]
⇒ [0.2691 , 0.3209]
So, 95% confidence interval = [0.2691 , 0.3209]
The numbers in this interval represent that we are 95% confident that the population proportion will lie between 0.2691 and 0.3209.
(d) Assumptions needed for constructing a confidence interval are;
- The data must be sampled randomly.
- Sample values must be independent of each other.
- Data must follow normal distribution.