ST 509 Sample Questions - Test 2
Topics Distribution of the sample mean. Central Limit Theorem. Confidence intervals for a population mean. Confidence intervals for a population proportion. Sample size for a given confidence level and margin of error (proportions). Poll articles. Hypotheses tests for a mean, and differences in means (independent and paired samples). Sample size and power of a test. Type I and Type II errors. You will be given a table of normal probabilities. You may wish to be familiar with the follow formulae and their application.
x ± t! 2, n"1 s
n ;
( x1 " x2 ) ± t! 2, #
2 s12 s2 + n1 n2
;
p ± z! 2
p (1" p ) n
$ z! 2 ' ; n=& p (1" p ) % m ) (
2
1. _____ A confidence interval for the mean
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_____ Referring to Question #10 above, which of the following best describes why you might be cautious in relying on these results? (A) The sample size is too small to make any reliable inference about the entire population. (B) Silly questions sometimes generate silly responses, not true opinions. (C) The respondents may not be a representative sample of any population of interest. (D) Newspapers tend to skew results to fit their own agenda.
12. _____ For a given population, confidence intervals constructed from larger samples tend to be narrower than those constructed from smaller samples. Which statement below best describes why this is true? (A) The variability of the sample mean is less for larger samples. (B) The z-value for larger samples tends to be more accurate. (C) The population variance is larger for large populations. (D) As the sample size increases, the z-value (or t-value) becomes smaller. A machine dispenses potato chips into bags that are advertised as containing one pound of product. To be on the safe side, the machine is supposed to be calibrated to dispense 16.07 ounces per bag, and from long time observation, the distribution of the fill-weights is known to be approximately normal and the process is known to have a standard deviation of 0.15 ounces.
13. _____ If the machine is properly calibrated, what proportions of bags will be underweight?
(A) 0.32 (B)
· How were measures of central tendency used in the study? Did the study use the most appropriate measure of central tendency for the given data? Why or why not?
2. In order to determine the average amount spent in November on Amazon.com a random sample of 144 Amazon accounts were selected. The sample mean amount spent in November was $250 with a standard deviation of $25. Assuming that the population standard deviation is unknown, what is a 95% confidence interval for the population mean amount spent on Amazon.com in November?
Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions.
B. 95% confidence intervals for the proportion of all students, the proportion of all male students, and the proportion of all female students who were involved in copying off the Internet is provided in the following table.
Consider the following scenario in answering questions 5 through 7. In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7.
The standard deviation of the sample was 6.2 weeks. Construct a 95 percent confidence interval for the population mean. Is it reasonable that the population mean is 28 weeks? Justify your answer.
1. A researcher is interested in whether students who attend private high schools have higher average SAT Scores than students in the general population. A random sample of 90 students at a private high school is tested and and a mean SAT score of 1030 is obtained. The average score for public high school student is 1000 (σ= 200).
2. At 95% confidence, use the p-value approach and test to determine if the average yearly income of marketing managers in the East is significantly different from the West.
The customers in this case study have complained that the bottling company provides less than the advertised sixteen ounces of product. They need to determine if there is enough evidence to conclude the soda bottles do not contain sixteen ounces. The sample size of sodas is 30 and has a mean of 14.9. The standard deviation is found to be 0.55. With these calculations and a confidence level of 95%, the confidence interval would be 0.2. There is a 95% certainty that the true population mean falls within the range of 14.7 to 15.1.
I strongly agree with all of the statements that I stated above. If the surveys had only been composed of those questions, the results have been the same to me. Honestly I don't know why but these statement seems like common sense to me to strongly
20) In a two-sample test of means for independent samples, we use the z distribution when…A. the population standard deviations are equalB. both populations have at least 4,000 observationsC. both population standard deviations are knownD. nB and n(1-B) are both greater than 5
Find the probability that a random sample of 5 airplanes exceeds a mean of 206.5 feet. Draw a Normal Graph of the data. (5)
In chapter 7 we discussed how to make inferences about a population parameter based on a sample statistic. While this can be useful, it has severe limitations. In Chapter 8, we expand our toolbox to include Confidence Intervals. Instead of basing our inference on a single value, a point estimate, a Confidence Interval provides a range of values, an interval, which – at a certain level of confidence (90%, 95%, etc.) – contains the true population parameter. Having a range of values to make inferences about the population provides much more room for accuracy than making an inference off of only one value.
The mean for variable 1 (Southern Africa) is 2.48. The mean for variable 2 (North Africa) is 2.28. The standard deviation for variable 1 is 1.077 and for variable 2, 9.68. The number of participants in each condition variable 1 N = 16922 and variable 2 N = 5466.
According to the author, the data collected for this article was obtained by systematic random samples during a 4-week reporting period. The