Practice Set 3

# Practice Set 3

1. Let x be a continuous random variable. What is the probability that x assumes a single value, such as a (use numerical value)?

2. The following are the three main characteristics of a normal distribution.

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3. For the standard normal distribution, find the area within one standard deviation of the

mean that is, the area between Î¼ âˆ’ Ïƒ and Î¼ + Ïƒ. Round to four decimal places.

4. Find the area under the standard normal curve. Round to four decimal places.

• a)between z = 0 and z = 1.95
• b)between z = 0 and z = âˆ’2.05
• c)between z = 1.15 and z = 2.37
• d)from z = âˆ’1.53 to z = âˆ’2.88
• e)from z = âˆ’1.67 to z = 2.24
1. The probability distribution of the population data is called the (1) ________. Table 7.2 in the text provides an example of it. The probability distribution of a sample statistic is called its (2) _________. Table 7.5 in the text provides an example it.
1. Probability distribution
2. Population distribution
3. Normal distribution
4. Sampling distribution

6. ___________ is the difference between the value of the sample statistic and the value of the corresponding population parameter, assuming that the sample is random and no non-sampling error has been made. Example 7â€“1 in the text displays sampling error. Sampling error occurs only in sample surveys.

7. Consider the following population of 10 numbers. 20 25 13 19 9 15 11 7 17 30

• a)Find the population mean. Round to two decimal places.
• b)Rich selected one sample of nine numbers from this population. The sample included the numbers 20, 25, 13, 9, 15, 11, 7, 17, and 30. Calculate sampling error for this sample. Round to decimal places.

8. Fill in the blank. The F distribution is ________ and skewed to the right. The F distribution has two numbers of degrees of freedom: df for the numerator and df for the denominator. The units of an F distribution, denoted by F, are nonnegative.

9. Find the critical value of F for the following. Round to two decimal places.

• a)df = (3, 3) and area in the right tail = .05
• b)df = (3, 10) and area in the right tail = .05
• c)df = (3, 30) and area in the right tail = .05

10. The following ANOVA table, based on information obtained for three samples selected from three independent populations that are normally distributed with equal variances, has a few missing values.

 Source of Variation Degrees of Freedom Sum of Squares Mean Square Value of the Test Statistic Between 2 2) 19.2813 Within 1) 89.3677 3) F = ___5)__ = 7) 6) Total 12 4)

Refer to Chapter 12, Example 12-2 and Tables 12.3 & 12.4, page 490.

• a)Find the missing values 1) â€“ 7) and complete the ANOVA table. Round to four decimal places.
• b)Using Î± = .01, what is your conclusion for the test with the null hypothesis that the means of the three populations are all equal against the alternative hypothesis that the means of the three populations are not all equal? Select from following:
1. Reject H0. Conclude that the means of the three populations are equal.
2. Reject H0. Conclude that the means of the three populations are not equal.
3. Do not reject H0. Conclude that the means of the three populations are equal.
4. Do not reject H0. Conclude that the means are of the three populations are not equal.

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