The report of a sample survey of 1014 adults says, “with 95% confidence, between 9% and 15% of all Americans expect to spend more on gifts this year than last year.”
The report of a sample survey of 1014 adults says, “with 95% confidence, between 9% and 15% of all Americans expect to spend more on gifts this year than last year.”
What does the phrase “95% confidence” mean?
The method used to get the interval 9% to 15%, when used over and over again, produces intervals which include the true population proportion 95% of the time.
95% of all Americans will spend between 9% and 15% more than what they spent last year.
9% to 15% of all Americans will spend 95% of what they spent last year.
There is a 95% chance that the percent who expect to spend more is between 9% and 15%.
Question 2What is the critical value of t for a 90% confidence interval with df = 14? (Assume a 2-tailed test)
2.62449
2.14479
1.761310
1.345030
Question 3What is the critical value for a 95% confidence interval based on a sample size of 20? (Population standard deviation is unknown). (Assume a 2-tailed test)
1.724718
1.729133
2.09302
2.08596
Question 4A survey of 30 random shoppers found a 95% confidence interval that shoppers will spend between $24.50 and $28.30.
A second survey surveyed 25 random shoppers.
The second interval will be narrower because the sample size is smaller and this creates less uncertainty.
The second interval will be wider because the sample size is smaller and this creates more uncertainty.
The second interval will be wider because it is likely that there are more outliers.
The second interval will be narrower because it is likely that there are less outliers.
Question 5A survey of 495 citizens found that 373 of them favor a new bill introduced by the city.
We want to find a 95% confidence interval for the true proportion of the population who favor the bill.
What is the lower limit of the interval? (Round to 3 decimal digits)
Question 6Compute a 95% confidence interval for the population mean, based on the sample numbers 21, 28, 33, 34, 25, 26, and 135.
Which table do we use to find the margin of error?
Z-Table
T-Table
G-Table
F-Table
Question 7Compute a 95% confidence interval for the population mean, based on the sample numbers 21, 28, 33, 34, 25, 26, and 135.
What is the Critical value? (Get 4 decimal digits).
2.5706
3.7074
2.4469
2.3646
Question 8Compute a 95% confidence interval for the population mean, based on the sample numbers 21, 28, 33, 34, 25, 26, and 135.
What is the margin of error? (Round to two decimal digits)
29.57
37.69
38.80
41.83
Question 9 Compute a 95% confidence interval for the population mean, based on the sample numbers 21, 28, 33, 34, 25, 26, and 135.
Find the lower and upper limits of the interval.
Lower – 15.449; Upper – 67.174
Lower – 20.492; Upper – 40.876
Lower – 18.925; Upper – 50.741
Lower – 5.449; Upper – 80.837
Question 10 Change the last value to 27 and re-compute the confidence interval.
The numbers now are: 21, 28, 33, 34, 25, 26, and 27
Lower – 3.52; Upper – 41.929
Lower – 23.52; Upper – 31.909
Lower – 22.32; Upper – 35.861
Lower – 19.73; Upper – 51.994
Question 11What is an outlier and how does it affect the confidence interval?
An outlier stretches the interval because it increases the standard deviation
An outlier compacts the interval because it increases the standard deviation
An outlier stretches the interval because it decreases the standard deviation
An outlier compacts the interval because it decreases the standard deviation
Question 12 The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the university indicates that x(bar) = $315.40 and s = $43.20.
Using a significance level of .1, what are the boundaries of the confidence interval?
302.438 – 326.184
300.618 – 330.182
297.485 – 327.820
282.871 – 338.475
Question 13The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the university indicates that x(bar) = $315.40 and s = $43.20.
A mean that is not in a confidence interval is rejected by the confidence interval, and we say the evidence against the mean is significant. At the 0.10 level of significance, is there evidence against mean $300?
No, because 300 is below the lower limit of the confidence interval
Yes, because 300 is below the lower limit of the confidence interval
No, because 300 is in the confidence interval
Yes, because 300 is in the confidence interval
Question 14 The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the university indicates that x(bar) = $315.40 and s = $75. (Note the sample standard deviation is different from the first part).
A mean that is in a confidence interval is not rejected by the confidence interval, and we say the evidence against the mean is not significant. At the 0.05 level of significance, is there evidence against mean $300?
No, because 300 is below the lower limit of the confidence interval
Yes, because 300 is below the lower limit of the confidence interval
No, because 300 is in the confidence interval
Yes, because 300 is in the confidence interval
Question 15 Explain the difference between parts A and C. In both parts we are asked whether or not there is evidence that the population mean was over $300.
In part A: x(bar) = $315.40; s = $43.2; Sample size = 25
In part C: x(bar) = $315.40; s = $75; Sample size = 25
The larger mean adds uncertainty in the sample. The sample may have had some outliers.
The smaller mean adds uncertainty in the sample. The sample may have had some outliers.
The larger standard deviation adds uncertainty in the sample. The sample may have had some outliers.
The smaller standard deviation adds uncertainty in the sample. The sample may have had some outliers.
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