 # Statistics Questions

## Question

Part 1
1) ____   A range of values used to estimate the true value of a population parameter is called:
a) a proportion b) a point estimate c) a confidence interval d) alpha

2) ____ The number on the border line separating sample statistics that are likely to occur from those that are unlikely to occur is the:
a) degree of confidence b) critical value c) margin of error d) sample value

3) ____ All of the following are considered unbiased estimators of a population except:
a) variance b) standard deviation c) proportion d) mean

4) ____ All of the following are examples of test statistics except:
a) alpha b) critical z scores c) critical t values d) chi-squared values

5) ___ A null hypothesis is a statement that the value of a population parameter is ___ a claimed parameter.
a) falsely attributed to b) greater than c) equal to d) less than

6) ____ In hypothesis testing, the area under the curve associated with alpha can be located under one or two tails depending on the test. Another name for the area under the curve associated with alpha is:
a) test statistic b) significance level c) P-value d) critical region

7) _____ The standard procedure of hypothesis testing requires that we directly test the:
a) test statistic b) alpha value c) P-Value d) null hypothesis

8) _____ When the values of one variable are somehow associated with the values of another variable, a ____ exists.
a) correlation b) computation c) requirement d) regression

9) ____ When the linear correlation coefficient r equals zero, there is:
a) a positive correlation     b) a negative correlation c) no correlation d) a nonlinear relationship

10) ____ In order to use a regression equation as a good prediction model, all of the following must be true except:
a) the regression lined graphed in the scatterplot shows that the line fits the points well.
b) there are at least 3 outliers.
c) r indicates that there is a linear correlation.
d) the prediction is not much beyond the scope of the available sample data.

Part 2
1) Find the critical value tα/2 for n = 20 and α = 0.05. _______
2) Find the critical value zα/2 for n = 20 and α = 0.10. _______
3) Find the sample size required to estimate the percentage of college students who use student loans to help fund their tuition. Assume that we want 95% confidence that the proportion from the sample is within two percentage points of the true population percentage. _______
4) In a survey of 1000 online statistics students, 400 were wearing shoes during class. Find the margin of error that corresponds to a 95% confidence level for this proportion. ___+/- ___
5) In a poll of 600 randomly selected subjects, 240 answered “yes” when asked if they planned to vote in a state election. What is the best point estimate of the population proportion of all who plan to vote in that election? _____
6) In a poll of 600 randomly selected subjects, 240 answered “yes” when asked if they planned to vote in a state election. Construct a 95% confidence interval estimate of the proportion of all who plan to vote in that election.    ____
7)   Find a 95% confidence interval for the braking distances of a single random sample of cars given n = 32; the sample mean = 137 ft; and the population standard deviation is known to be 7 ft. __________
8) How many daily rainfall amounts in Boston must be randomly selected to estimate the mean daily rainfall amount? We want 99% confidence that the sample mean is within .010 in. of the population mean, and the population standard deviation is known to be .212 in. _______
9) In a test of the Atkins weight loss program, 40 individuals participated in a randomized trial with overweight adults. After 12 months, the mean weight loss was found to be 2.1 lb, with a sample standard deviation of 4.8 lb.
a) What is the best point estimate of the population mean weight loss of all overweight adults who follow the Atkins program? _______
b) Construct a 99% confidence interval estimate of the mean weight loss for all such subjects. _____
10) Find the critical values in the chi-square distribution that correspond to a 95% confidence interval where n = 9.
a) X2L: _______ b) X2R: _______

Part 3
1) In hypothesis testing, we use a test statistic to find a P-value. We can compare the area of that P-value to that of the given alpha. If the P-value is ≤ α (the P is low), we will _________.
2) If the test statistic does not fall within the critical region, we __________.
3) If you find the P-value > α, ______________.
4) If you are conducting a right-tailed test with a critical z-score of 1.645, and have a test statistic z-score of 3.21, you would __________.
5) If you are conducting a left-tailed test with a critical chi-square value of 23.269, and have a test statistic of 18.483, you would _________.

Part 4
1) Claim: the proportion of males is greater than .5. Express your hypothesis in symbolic form (in terms of ‘p’):
a) H0: _____ b) H1: _____

2) For a normal distribution, find the critical z-values for a two-tailed test with α = .01. ________

3) For a normal distribution, find the critical z-score value for α = .01 and H1 is p > .5. _________

4) Find the P-value of the following. Use a .05 significance level and state the conclusion about the null hypothesis (Write either ‘reject the null hypotheses’ or ‘fail to reject the null hypothesis’). It may be helpful to sketch the curve on your scratch paper.
a) The test statistic in a left-tailed test is z = -1.25.
P-Value: _______
Conclusion: _________________

b) With H1: p ≠ .707, the test statistic is z = -2.75.
P-Value: ________
Conclusion: ___________

5) A recent study showed that 53% of college applications were submitted online. Assume this result is based on a simple random sample of 1000 college applications, with 530 submitted online. Use a .01 significance level to test the claim that among all college applications, the percentage submitted online is equal to 50%. You may choose to sketch the curve on your scratch paper for visual support.
a) What is the proportion of applications submitted online? _____
b) The null hypothesis includes the equality.
Claim: the percentage of applications submitted online is equal to 50%. State the null and alternative hypothesis (in terms of ‘p’):
H0: ______ H1: _________
This will be a (right-tailed, left-tailed, or two-tailed) test: __________

c) The test statistic based on the survey results is the z-score: ________
d) The critical value based on the type of test (right, left, or two-tailed) and the alpha is the z-score: _+/-____
e) The P-value based on the test statistic is: __________
f) What is the conclusion? (use this space to write 2- 3 sentences for your conclusion)
6) Researchers collected a simple random sample of the times that 81 college students required to earn their bachelor’s degrees. The sample has a mean of 4.8 years and a standard deviation of 2.2 years. Use a .05 significance level to test the claim that the mean time for all college students is greater than 4.5 years (the population standard deviation is unknown). You may choose to sketch the curve on your scratch paper for visual support.
a) This is a claim about a mean with an unknown population standard deviation. It is a simple random sample with n > 30. What type of distribution will you need to use? _____
b) The null hypothesis includes the equality.
Claim: the mean time for all college students to earn a degree is greater than 4.5 years. State the null and alternative hypothesis (in terms of ‘μ’):
H0: _____ H1: _______
This will be a (right-tailed, left-tailed, or two-tailed) test: ___________
d) The test statistic based on the survey results is: ________
e) The critical value based on the type of test (right, left, or two-tailed) and the alpha is: ______
f) The P-value based on the test statistic is: _________
g) What is the conclusion? (use this space to write 2- 3 sentences for your conclusion)

Part 5
1) Which value for r indicates a stronger correlation: r = .003 or r = -.897? ______
2) A scatterplot showing a distinct pattern of bivariate data rising to the right is said to have (nonlinear, positive, or negative) correlation: ________
3) The value for r is always between what two numbers (inclusive)? ____
4) True or False: Correlation explicitly proves causality. ______________
5) Given the critical values of r = ± .811, and a sample data statistic showing r = .988, would you find there to be a correlation (yes/ no)? ______
6) When we graph a regression line that rises to the left, we know that the r has a (nonlinear, positive, or negative) value. ________ The r value is related to the slope of a line.
7) If the regression equation does not appear to be useful for making predictions, the best predicted value of a variable is its __________________, which is its sample mean.

## Solution Preview

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Part 1
1) __C__ A range of values used to estimate the true value of a population parameter is called:
a) a proportion b) a point estimate c) a confidence interval d) alpha

2) __B__ The number on the border line separating sample statistics that are likely to occur from those that are unlikely to occur is the:
a) degree of confidence b) critical value c) margin of error d) sample value

3) __B__ All of the following are considered unbiased estimators of a population except:
a) variance b) standard deviation c) proportion d) mean...
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