Part I True-False Statements: Fill in T or F (4 points each)

1. Significant difference in a statistical sense means that the observed, or apparent, difference is of practical importance and should not be neglected. ___
2. For a fixed sample size, testing at the 1% level instead of the 5% level will increase the chance of committing a Type II error. ___
3. If random samples of size 35 are drawn from a nonnormal population, the means of these samples will be approximately normally distributed. ___
4. When a 95% confidence interval around a point estimate of excludes _o, H_o should not be rejected at the 0.05 level. ___
5. A P-value greater than 0.05 is proof that the null hypothesis is true. ___

Part II Fill in the correct choice (4 points each)

1. Part 1: As the minimum detectable difference increases, the power of a significance test ___.

XXX

1. Increases

1. Decreases

.

Part 2: As the sample size increases, the power of a significance test ___.

XXX

1. Increases

1. Decreases

1. Part 1: Fill in the correct choices:

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Statistic? ___

Parameter? ___

1. Characteristic of a population (constant)

b) Characteristic of a random sample drawn from a population (vary from sample to sample)

Part 2: Complete the following statement regarding the relationship between the Z and t distributions.

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Z is a special case of t as the number of degrees of freedom approaches ___________.

1. What is the only way to increase power of a significance test when lowering the probability of committing a Type I error? ___

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1. Increase the sample size

1. Reduce the variance

1. Increase the minimum detectable difference

1. Part 1: In what circumstance is the median superior to the mean as an indicator of central tendency? ___

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1. When dealing with outliers

1. When dealing with bimodal distributions

1. When dealing with skewed distributions

Part 2: In order to determine if a distribution is approximately normal we need to know the ___.

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1. Skewness

1. Kurtosis

1. Variance

1. Skewness and Variance

1. Kurtosis and Variance

1. Skewness and kurtosis

1. Skewness, Kurtosis, and Variance

1. Part 1: As the sample size increases, the width of a 95% confidence interval ___.

XXX

1. Increases

1. Decreases

.

Part 2: In performing an ANOVA with a fixed total sample size, as the number of groups being compared increases, the power ___.

XXX

1. Decreases

1. Increases

1. When comparing three means, why is ANOVA used instead of performing three separate t-tests? ___

XXX

1. To increase power

1. To prevent inflation of the type I error

1. Part 1: Fill in the correct choices concerning nonparametric alternatives to the:

Independent 2-sample t-test? ___

Paired-sample t-test? ___

One-way ANOVA? ___

Randomized block ANOVA? ___

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1. Kruskal-Wallis test

1. Mann-Whitney test

1. Friedman's test

1. Wilcoxon paired-sample test

Part 2: Under what circumstances are nonparametric tests employed? ___

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1. When there is a violation of the assumption of normality

1. When there is a violation of the assumption of equality of variance

1. When dealing with ordinal data

d) All of the above

1. If the null hypothesis is not rejected in a significance test, what must be known for one to accept Ho? ___

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1. The probability of committing a type I error

1. The probability of committing a type II error

1. As health commissioner of city A, you have decided to implement a $ 20 million exercise program for elementary school children if there was 95% confidence that the mean resting heart rate in this population was different from 80 beats/min. Using a random sample of 45 elementary school children, the estimated mean heart rate was found to be 86.5 beats/min with a 95% confidence interval from 79.1 to 93.9 beats/min. What is your decision? ___

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1. Implement program

1. Do not implement program

1. When planning a statistical analysis, what takes precedence? ___

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1. Minimizing bias

1. Maximizing power

Part III Problems (20 points each)

1. The health commissioner of city B postulated that the mean diastolic blood pressure (DBP) in a population of patients diagnosed as hypertensive was 100 mm Hg. Wishing to test this null hypothesis, a random sample of 11 subjects was drawn from this target population.

The results were as follows (DBP in mm Hg):

96, 114, 125, 105, 97, 96, 131, 117, 107, 111, 123

Using the attached SAS file (SASmidterm1.sas), perform a one-sample t-test

Assume the sample was drawn from a normally distributed population.

Use = 0.05 (two-tailed) and assume 80% power.

a) State the null and alternative hypotheses.

XXX

b) List the critical value

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c) Replacing the response lines, report your decision (reject Ho and accept Ha OR fail to reject Ho) based on the critical value, P-value, and 95% confidence interval for the population mean:

__________________________________________________________________________

XXX

__________________________________________________________________________

XXX

__________________________________________________________________________

XXX

d) If the decision was to fail to reject Ho, can Ho be accepted?

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2. A study was conducted among children aged 8-10 to determine if resting heart rate differed between males and females. Independent samples of 8 females and 8 males were selected from the two respective populations.

The results were as follows (heart rates in beats/min):

Females 71, 80, 80, 75, 78, 77, 81, 82

Males 71, 81, 79, 74, 73, 78, 71, 74

Using the attached SAS file (SASmidterm2.sas), perform a two-sample t-test.

Assume normality and equal variance.Use = 0.05 (two-tailed) and assume 80% power.

1. State the null and alternative hypotheses.

1. List the critical value.

c) Replacing the response lines, report your decision (reject Ho and accept Ha OR fail to reject Ho) based on the critical value, P-value, and 95% confidence interval for the difference between the population means.

d) If the decision was to fail to reject Ho, can Ho be accepted?

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