In 2007 a Pew survey asked 1447 Internet users about their sources of news and information about science. Among those who had broadband access at home, 34% said they would turn to the internet for most of their science news. The resport on this survey claims that this is not significantly different from the percentage (33%) who said they ordinarily get their science news from television. What does it mean to say that the difference is not significant?
Watch the video below if you need to understand better what statistical significance means. Skip if you don't.
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Question 2
2.
We have calculated a confidence interval based upon a sample of n=200. Now we want to get a better estimate with a margin of error only 1/5 as large. We need a new sample with n at least...
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Question 3
3.
A certain population is strongly skewed to the right. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one?
I. The distribution of our sample will be closer to normal.
II. The sampling model of the sample means will be closer to normal.
III. The variability of the sample means will be greater.
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Question 4
4.
Which is true about a 95% confidence interval based on a given sample?
I. The interval contains 95% of the population.
II. Results from 95% of all samples will lie in the interval.
III. The interval is narrower than a 98% confidence interval would be.
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Question 5
5.
A truck company wants on-time delivery for 98% of the parts they order from a metal manufacturing plant. They have been ordering from Hudson Manufacturing but will switch to a new, cheaper manufacturer (Steel-R-Us) unless there is evidence that this new manufacturer cannot meet the 98% on-time goal. As a test the truck company purchases a random samples of metal parts from Steel-R-Us, and then determines if these parts were delivered on-time. Which hypotheses should they test?
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Question 6
6.
We are about to test a hypothesis using data from a well-designed study. Which is true?
I. A small P-value would be strong evidence against the null hypothesis.
II. We can set a higher standard of proof by choosing an alpha level of 10% instead of 5%
III. If we reduce the alpha level, we reduce the power of the test.
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Question 7
7.
A pharmaceutical company investigating whether drug stores are less likely than food markets to remove over-the-counter drugs from the shelves when the drugs are past the expiration date found a P-value of 2.8%. This means that:
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Question 8
8.
What is the correct interpretation of the p-value in the context of #7?
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Question 9
9.
The Dean of Education at a university wants to test a hypothesis that the proportion of this university's pre-service teachers have qualified for paid internship positions this year is less than 40%. Based on the data he collected, he creates a 90% confidence interval of (33%, 41%). Could this confidence interval be used to test the hypothesis
at the alpha level of 0.05?
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Question 10
10.
Suppose that a conveyor used to sort packages by size does not work properly. We test the conveyor on several packages (with a null hypothesis that the sort is incorrect) and our data results in a P-value of 0.016. What probably happens as a result of our testing?
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Question 11
11.
We test the hypothesis that p=35% verus p<35%. We don't know it but actually p=26%. With which sample size and significance level will our test have the greatest power?
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Question 12
12.
#11-15 refer to the scenario below.
The owner of a small clothing store is concerned that only 28% of people who enter her store actually buy something. A marketing salesman suggests that she invest in a new line of celebrity mannequins. He loans her several different "people" to scatter around the store for a two-week trial period. The owner carefully counts how many shoppers enter the store and how many buy something so that at the end of the trial she can decide if she'll purchase the mannequins.
In context, describe a Type 1 error and the impact such an error would have on the store.
Describe a Type 2 error and the impact such an error would have on the store.
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Question 13
13.
Based on the data that she collected during the trial, the store's owner found that a 98% confidence interval for the proportion of all shoppers who might buy something was (27%, 35%). What conclusion should she reach about the mannequins? Explain.
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Question 14
14.
What alpha level did the store's owner use?
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Question 15
15.
Describe to the owner an advantage and a disadvantage of using an alpha level of 5% instead.
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Question 16
16.
The owner talked the salesman into extending the trial period so that she can base her decision on data for a full month. Will the power of the test...
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Question 17
17.
According to the Centers for Disease Control and Prevention (CDC) web site, 50% of high school students have never smoked a cigarette. Taya wonders whether this national result holds true in her large, urban high school. For her AP Stats project, she surveys an SRS of 150 students from her school. She gets responses from all 150 students and 90 say that they have never smoked a cigarette. Does this provide evidence that students in her high school smoke at a lower rate than the CDC's estimate? Use an alpha level of 0.05.
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Question 18
18.
Create a confidence interval to estimate the true proportion of students at her high school who have never smoked a cigarette.