Confidence Intervals
Practice Problems for Confidence Intervals
X ± Z σ/n ; X ± t s/n ; p ± Z (p(1-p)/n)
1. A press release issued by our university claims that West Chester students study at least as much as the national average for students at four year universities. Across the nation, 73 percent of all students at four year universities study at least four hours per week. Seventy percent of one hundred randomly selected West Chester students surveyed claimed to study more than four hours per week. Should the University retract its previous statement? Explain why or why not.
We can be 90 percent sure that the percentage of all WCU students who study at least 4 hours per week is :
.7 1.64 (.7*.3/100)
.7 .07. so 63 to 77%. We can’t be sure the statement is correct, but it might be so I would not instruct the University to retract its statement.
2. A car manufacturer is considering switching to a new brand of brake shoes. To test the shoes, the manufacturer submits the shoes to a heat test. The higher the failure temperature, the better the shoe. Past experience has shown that heat failure temperature is normally distributed. A sample of five shoes failed at the following temperatures: 300, 310, 280, 350 and 260F. If the old shoes, which are considered reliable fail at an average temperature of 290F, should the company make the switch? Explain your answer.
Using the t distribution, we can be 95 percent sure that the average failure temperature of the new shoes is: 300 2.776(33.91/5) (that t is based on .025 and d.f. = 4)
= 300 42 258 to 342. We cannot be sure that the new pads are better (though they may be) sow we should not switch)
3. A government researcher is trying to determine whether or not a new car model averages at least 30 miles per gallon in the city. If it does, the government will give the manufacturer a $100 tax break per car. From previous studies, the standard deviation of mpg is known to be 5 mpg. If
X ± Z σ/n ; X ± t s/n ; p ± Z (p(1-p)/n)
1. A press release issued by our university claims that West Chester students study at least as much as the national average for students at four year universities. Across the nation, 73 percent of all students at four year universities study at least four hours per week. Seventy percent of one hundred randomly selected West Chester students surveyed claimed to study more than four hours per week. Should the University retract its previous statement? Explain why or why not.
We can be 90 percent sure that the percentage of all WCU students who study at least 4 hours per week is :
.7 1.64 (.7*.3/100)
.7 .07. so 63 to 77%. We can’t be sure the statement is correct, but it might be so I would not instruct the University to retract its statement.
2. A car manufacturer is considering switching to a new brand of brake shoes. To test the shoes, the manufacturer submits the shoes to a heat test. The higher the failure temperature, the better the shoe. Past experience has shown that heat failure temperature is normally distributed. A sample of five shoes failed at the following temperatures: 300, 310, 280, 350 and 260F. If the old shoes, which are considered reliable fail at an average temperature of 290F, should the company make the switch? Explain your answer.
Using the t distribution, we can be 95 percent sure that the average failure temperature of the new shoes is: 300 2.776(33.91/5) (that t is based on .025 and d.f. = 4)
= 300 42 258 to 342. We cannot be sure that the new pads are better (though they may be) sow we should not switch)
3. A government researcher is trying to determine whether or not a new car model averages at least 30 miles per gallon in the city. If it does, the government will give the manufacturer a $100 tax break per car. From previous studies, the standard deviation of mpg is known to be 5 mpg. If