# Stat 200 | Mathematics homework help

Review 1. Which of the following statements regarding the t distribution is true?
A) The total area under a t-curve with 10 degrees of freedom is greater than the area under the standard normal curve (i.e., z distribution).
B) The t-curve with 10 degrees of freedom is flatter and the tails are higher than the standard normal curve (i.e., z distribution).
C) The t-curve with 10 degrees of freedom more closely resembles the standard normal curve (i.e., z distirbution) than the t-curve with 50 degrees of freedom.

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Review 2. Which of the following statements best describes the relationship between a parameter and a statistic?
A) A parameter is used to estimate a statistic.
B) A statistic is used to estimate a parameter.
C) A parameter has a sampling distribution with the statistic as its mean.

Review 3. For which of the following situations would the Rule for Sample Proportions not apply?
In other words, in which of the following situations would it be inappropriate to use the normal approximation method?
A) A random sample of 100 is taken from a population in which the proportion with the trait of interest is 0.98.
B) A random sample of 50 is taken from a population in which the proportion with the trait of interest is 0.50.
C) A binomial experiment is done with n = 500 and p = 0.9.

Review 4. Suppose time spent on email for employees in a normal work day is independent and normally distributed with an average of 57 minutes and standard deviation of 12 minutes. What is the standard deviation of the sample mean in a random sample of n = 36 employees?
A) 1.58 minutes
B) 2.00 minutes
C) 9.50 minutes
D) 0.33 minutes

Review 5. Suppose that a confidence interval for a population proportion is to be calculated. For a sample size n = 100 and sample proportion  = 0.80 what is the approximate margin of error for a 95% confidence interval?
A) 0.1600
B) 0.0032
C) 0.0800
D) 0.0400

Review 6. When the 2000 General Social Survey asked participants if they would be willing to accept cuts in their standard of living to protect the environment, 350 of 1400 participants responded “yes.”  A 98% confidence interval for the proportion of all Americans who would accept cuts in their standard of living to protect the environment is:
A) (0.2309, 0.2691)
B) (0.2273, 0.2727)
C) (0.2230, 0.2770)
D) (0.2201, 0.2799)

Review 7. The heights of a sample of n = 101 3rd grade school boys will be used to create a 99% confidence interval for the mean height of all 3rd grade boys. The sample mean is 48 inches and sample standard deviation is 5 inches. Which of the following provides a 99% confidence interval for the population mean?
A) 48 ± (2.626)(5)
B) 48 ± (2.626)(0.5)
C) 48 ± (2.626)(1)
D) 48 ± (2.626)(2.5)

Review 8. A group of researchers want to know if, on average, professors sit for more than 6 hours a day. Using mu to represent population mean of sitting hours during the day for high blood pressure patients and mu-hat to represent the sample mean of the 100 patients, what is a correct statement of null hypothesis for this study?
A) mu = 6
B) mu-hat > 6
C) mu >= 6
D) mu-hat = 6

Review 9. A random sample of 100 light bulbs was examined to test if the mean life of all light bulbs of this brand is different from 5000 hours. The null hypothesis is that the population mean is 5000 hours. The alternative hypothesis is that the population mean is not 5000 hours. Suppose the mean of the sample is 5200 hours. How would a p-value be calculated in this situation?
A) Find the chance of the sample mean to be 5200 or more hours, calculated assuming the true population mean is smaller than 5000.
B) Find the chance of the sample mean to be 5200 or more hours, calculated assuming the true population mean is exactly 5000.
C) Find the chance of the sample mean to be 5200 or less hours, calculated assuming the true population mean is exactly 5000.
D) Find the chance of the sample mean to be 5200 or more hours, calculated assuming the true population mean is greater than 5000.

Review 10. Statistical significance occurs when
A) Sample statistics vary from the parameter value in the null hypothesis to the extent that it is unlikely that the results obtained were due to random sampling error.
B) Sample statistics vary from the parameter value in the null hypothesis to the extent that it is likely that the results obtained were due to random sampling error.
C) Sample statistics vary from the parameter value in the alternative hypothesis to the extent that it is unlikely that the results obtained were due to random sampling error.

Review 11. Based on the following output, what is the appropriate conclusion with a significance level of 0.05?
A) Reject the null hypothesis because the p-value is less than the significance level.
B) Fail to reject the null hypothesis because the p-value is less than the significance level.
C) Reject the null hypothesis because the p-value is greater than the significance level.
D) Fail to reject the null hypothesis because the p-value is greater than the significance level.

Review 12. How many Penn State World Campus Stat 200 students know how to compute a test statistic for proportions? On a recent midterm, 307 out of 330 students correctly computed a test statistic. What’s the test statistic for this proportion if you would like to test if the population proportion is lower than 0.95?
A) z = -1.64
B) z = -0.02
C) z = 0.01
D) z = 0.93

Review 13. At a company that produces dental cements, a scientist wants to determine whether teeth from cattle can be used in strength tests instead of teeth from people to save money during development of new formulas. The scientist knows that the mean adhesive strength for a particular dental cement is 18 MPa for human teeth. The scientist collects a random sample of 33 cattle teeth and tests the adhesive on them. The sample mean strength is 15 MPa. The sample standard deviation is 6 MPa. The scientist tests the alternative hypothesis that the adhesive strength on the cattle teeth is different from the known adhesive strength for human teeth. What is the value of the test statistic?
A) t = -0.5
B) t = 0.5
C) t = 2.87
D) t = -2.87

Review 14. Researchers are working to determine whether a new process increases the mean lifetime of automobile tires relative to a current specification. The researchers choose a p-value of 0.05. For 1 particular sample, the resultant data show that the lifetime increased when, in reality, the tires will not last longer on average than the current specification. Which of the following occurred in this scenario?
Researchers are working to determine whether a new process increases the mean lifetime of automobile tires. For one particular sample, the resultant data showed that the lifetime increased when, in reality, the tires will not last longer on average than the current specification. Which of the following occurred in this scenario?
A) Type I error
B) Type II error
C) Correct decision

Review 15. At a forest products company, a sample of 56 boards is cut into two pieces. One half receives an existing weather-resistance treatment while the other half receives a new weather-resistance treatment. The boards are placed in a chamber where they are exposed to levels of heat, moisture, and radiation. The strength of the boards is then measured. The mean of the differences is 1.94 with a standard deviation of 4.8. What is the value of the test statistic?
A) t = -3.02
B) t = 22.40
C) t = -22.40
D) t = 3.02

Review 16. A group of statistics students wanted to know if male and female college soccer players were different heights on average. The students took a random sample of 15 male and 15 female college soccer players, measured their heights, and conducted a two-tailed independent t-test. Their results were a t test statistic (df=28) of 3.13 and a p value of .0041.  With an alpha level of .05, what is the correct conclusion in relation to their research question?
A) Reject the null hypothesis. There is evidence that in the population male and female college soccer players have different mean heights.
B) Fail to reject the null hypothesis. There is evidence that in the population male and female college soccer players have different mean heights.
C) Fail to reject the null hypothesis. There is not evidence that in the population male and female college soccer players have different mean heights.
D) Reject the null hypothesis. There is not evidence that in the population male and female college soccer players have different mean heights.

Review 17. Which of the following is TRUE about hypothesis testing?
A) The test statistic is a population parameter.
B) Results are said to be statistically significant when the p value is greater than the alpha level.
C) Hypotheses are statements about the sample(s).
D) Hypothesis testing uses information from a sample to make an inference about a population.

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