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1. t-distribution Which of the following statements

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1. t-distribution

Which of the following statements is true with respect to the t – distribution?

1. The t – distribution is more spread out than the standard normal distribution

2. The t – distribution is symmetrical

3. The shape of the t – distribution depends on the number of degrees of freedom

4. All of the above

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2. Confidence interval for sample size 8

When finding a confidence interval for a population mean based on a sample of size 8, which assumption is made?

1. The population standard deviation, s is known.

2. The sampling distribution of z is normal.

3. The sampled population is approximately normal.

4. There is no special assumption made.

3. t-distribution degrees of freedom

As the degrees of freedom for the t-distribution increase, the distribution approaches the:

1. chi-square distribution.

2. t distribution.

3. normal distribution.

4. F distribution.

5. Characteristics of t-distribution

Which of the following statements is false?

1. The t distribution is symmetric about zero

2. The t distribution is more spread out than the standard normal distribution

3. As the degrees of freedom get smaller, the t-distribution’s dispersion gets smaller

4. The t distribution is mound-shaped

6. More characteristica of t-distrubution (Points: 10.0) Which of the following correctly describes Student’s t distribution?

1. It is a sampling distribution for a random variable, t, derived from a normally distributed population

2. It is single-peaked above the random variable’s mean, median, and mode of 1

3. It is always skewed to the right

4. All of the above

7. Small samples, unknown standard deviation

Which of the following statements is true when small samples are used to estimate the true population mean where the population standard deviation is unknown?

1. The standard normal distribution must be used to obtain the critical value

2. The t – distribution must be used to obtain the critical value

3. The margin of error for the confidence interval estimate tend to be very small

4. All of the above

8. t-distribution table

The t - distribution table in your text shows:

1. the area under a specified curve, defined by a given number of degrees of freedom , that lies to the left of a specified value of t

2. the area under a specified curve, defined by a given number of degrees of freedom, that lies to the right of a specified value of t

3. the heights of a specified curve, defined by a given number of degrees of freedom, at various specified values of t

4. specified values of t for different heights of a specified curve, defined by a given number of degrees of freedom

9. Confidence interval for 20 students (Points: 10.0) If you wish to estimate with 95% confidence the average number of miles that students living off – campus commute to classes every day, a random sample of 20 students produced a mean equal to 5.2 miles and a standard deviation of 3.05 miles. Then, the appropriate critical value is:

1. 1.96

2. 2.086

3. 2.093

4. 1.7291

10. Rejection region for t-test with sample size 20

Suppose that a t-test is being conducted at the 0.05 level of significance to test 0:5H 0 µ= vs. 1:5H 0 µ<. A sample of size 20 is randomly selected. The rejection region is:

1) 4. All of the above 2) 3. The sampled population is approximately normal. 3) 3. normal distribution. 4) Question missing 5) 4. The t distribution is mound-shaped 6) 1. It is a sampling distribution for a random variable, t, derived from a normally distributed population 7) 2. The t – distribution must be used to obtain the critical value 8) 2. the area under a specified curve, defined by a given number of degrees of freedom, that lies to the right of a specified value of t 9) 3. 2.093 10) 2. t < -1.729