# CIS 343 - T 1 A 95 confidence interval is wider than a 90...

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T 1. A 95% confidence interval is wider than a 90% confidence interval. F 2. A poll cannot have both selection bias and non response bias at the same time. T 1. A confidence interval will always include X F 2. Exclusion bias occurs when some questions in a survey are not answered and therefore the answer is excluded. F 3. The Central Limit Theorem says that the probability that X is closer to . F 1. A data point that is 2 SD’s away from the center is a typical data point. T 3. Response bias is when the response to a question is given incorrectly. T 1. A point estimate X can be far from the true value . F 2. The wider a confidence interval is the less confidence you have in it. F 3. Selection bias happens when the people selected to be polled refuse to answer selected questions in the survey. 4. On the normal curve Find the area a) between -1.25 and 0. Ans. = .5 - .1056 = .3944 b) between -.70 and 1.21 Ans. = .8869 - .2420 = .6449 Find z if the area c) to the left of z is .0764 Ans. z=-1.43, small area to left means z is negative, finding .0764 in the body of the z table gives z=-1.43 d) to the left of z is .9394 Ans. z=1.55, large area to left means z is positive, finding .9394 in the body of the z table gives z=1.55 6. Jake wants to learn Spanish on his own and every week studies either 2, 6, or 7 hours at random. His SD for studying Spanish is 2.16 hours per week. In one year find a range for the total number of hours he will spend on learning Spanish. This is a gambling problem in disguise. The box has three tickets 2,6,7 so the average of the box is μ=5, σ=2.16. Total hours for the year is the sum of each week. Expected(winnings)=nμ=52*5=260 SD(winnings)=√n*σ=√(52)*2.16=15.576 Rough range is 260±15.576 or 244.424 to 275.576 9. The President of Murray State wants a confidence interval for the average number of students who go to summer school at MSU. A sample of 8 summers yielded an average of 900 students with a standard deviation of 200 students. Find an 80% confidence interval. This is a t-confidenceinterval since the SD is connected to the sample size n. X ±t*s/√n With .8 in the middle gives .1 in the right tail and with 8-1=7df gives t=1.415 CI is 900±1.415*200/√8 CI is 900±100.06 or 799.94 to 1000.06

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9. a) Interpret the CI in words. We believe the true average number of students in summer school is between 799.94 and 1000.06 with 80% confidence. 9. b) Do you believe the true average could be as high as 1050 students? Explain. 1050 is outside the interval and would be considered too high for the true ave. 10. A psychologist says that looking at sunsets is good for your mental health. The psychologist wants to see now whether people in Kentucky or Missouri spend more time watching sunsets. The SD for watching sunsets in Kentucky is 3 hours per month per person, and in Missouri it is 2 hours per month per person. Since the SD is one and a half times bigger in Kentucky, he will sample one and a half as many people in Kentucky compared to Missouri. The sample size in Kentucky is 150 people and the sample size in Missouri is 100 people. The psychologist believes that the accuracy in the two states will be the same, do you agree? Explain.
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