## [answered] A sampling distribution of the means is a probability distr

Please answer the following statistics MCQ and True/False(Total 32 Questions).Only professor who have rating of 3 and above may proceed to answer these questions.
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1. A sampling distribution of the means is a probability distribution consisting of all possible

sample means of a given sample size selected from a population. (Points : 3)

True

False Question 2.2. According to the central limit theorem: (Points : 3)

the sampling distribution of the sample means will be skewed.

the sampling distribution of the sample means is approximately normally

distributed.

the population mean and the mean of all sample means are equal.

increasing sample size decreases the dispersion of the sampling distribution. Question 3.3. In the sampling distribution of the sample means, the standard

error of the mean will vary according to the size of the sample. As the

sample size, n, gets larger, the variability of the sampling distribution gets

larger. (Points : 3)

True

False Question 4.4. The central limit theorem states that if the sample size, n, is

sufficiently large, the sampling distribution of the means will be

approximately normal, even when the population is skewed or uniform.

(Points : 3)

True

False Question 5.5. According to the central limit theorem: (Points : 3)

the sampling distribution of the sample means will be skewed.

the sampling distribution of the sample means is uniform. increasing the sample size decreases the dispersion of the sampling distribution.

sample size is important when the population is not normally distributed. Question 6.6. The central limit theorem states that for a sufficiently large sample the

sampling distribution of the means of all possible samples of size n generated from the

population will be approximately normally distributed with the mean of the sampling

distribution equal to ?2 and the variance equal to ?2/n. (Points : 3)

True

False Question 7.7. In research, random sampling is necessary to avoid any form

of error. (Points : 3)

True

False Question 8.8. A collection of items, measurements, or entities taken from a

population in such a manner as to ensure each has the same chance of

being included is a simple random sample. (Points : 3)

True

False Question 9.9. Simple random sampling is the only method to ensure a

representative sample can the selected. (Points : 3)

True

False Question 10.10. Type I Error occurs when the null hypothesis is true but is

rejected. (Points : 3)

True False Question 11.11. When a decision is made to retain a false null hypothesis, a

Type II Error occurs. (Points : 3)

True

False Question 12.12. When selecting an alpha level to conduct a hypothesis test,

the researcher is determining the probability of making a Type I Error. (Points

: 3)

True

False Question 13.13. A sample of 2,000 union members was selected, and a survey recorded

their opinions regarding a proposed management union contract. A total of 1,600 members

were in favor of it. A 95% confidence interval estimated that the population proportion was

between 0.78 and 0.82. This indicates that about 80 out of 100 similarly constructed

intervals would include the population proportion. (Points : 3)

True

False Question 14.14. Knowing the population standard deviation, a 95%

confidence interval infers that the population mean: (Points : 3)

is between 0 and 100%.

is too large.

is within +/- 1.96 standard deviations of the sample mean.

is within +/- 1.96 standard errors of the sample mean. Question 15.15. A random sample of 42 college graduates revealed that

they worked an average of 5.5 years on the job before being promoted. The sample standard deviation was 1.1 years. Using the 0.99 degree of

confidence, what is the confidence interval for the population mean?

(Points : 3)

5.04 and 5.96

4.40 and 6.60

2.67 and 8.33

5.06 and 5.94 Question 16.16. For a null hypothesis, H0: ? = 4,000, if the 1% level of significance is

used and the z-test statistic is +6.00, what is our decision regarding the null

hypothesis? (Points : 3)

Do not reject the null hypothesis.

None apply.

Reject the alternative hypothesis.

Reject the null hypothesis. Question 17.17. For a one-tailed hypothesis test, the critical z value of the test statistic

is -2.33. Which of the following is true about the hypothesis test? (Points : 3)

a = 0.05 for a lower-tailed test

a = 0.01 for an upper-tailed test

a = 0.05 for an upper-tailed test

a = 0.01 for a lower-tailed test Question 18.18. The average cost of tuition and room and board at a small private

liberal arts college is reported to be \$8,500 per term, but a financial administrator believes

that the average cost is higher. A study conducted using 350 small liberal arts colleges

showed that the average cost per term is \$8,745. The population standard deviation is

\$1,200. Let ? = 0.05. What are the null and alternative hypotheses for this

study? (Points : 3)

H0: Mu &lt;/= \$9,000; H1: Mu &gt; \$9,000 H0: Mu &gt;/= \$8,500; H1: Mu &lt; \$8,500

H0: Mu &gt;/= \$9,000; H1: Mu &lt; \$9,000

H0: Mu &lt;/= \$8,500; H1: Mu &gt; \$8,500 Question 19.19. A random sample of size 15 is selected from a normal population. The

population standard deviation is unknown. Assume the null hypothesis indicates a two-tailed

test and the researcher decided to use the 0.10 significance level. For what values of t will

the null hypothesis not be rejected? (Points : 3)

To the left of -1.345 or to the right of 1.345

To the left of -1.645 or to the right of 1.645

To the left of -1.282 or to the right of 1.282

Between -1.761 and 1.761 Question 20.20. A hypothesis regarding the weight of newborn infants at a community

hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and

their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the

decision for a statistical significant change in average weights at birth at the 5% level of

significance? (Points : 3)

Reject the null hypothesis and conclude the mean is higher than 6.6 pounds.

Reject the null hypothesis and conclude the mean is lower than 6.6 pounds.

Fail to reject the null hypothesis.

Cannot calculate because the population standard deviation is unknown. Question 21.21. The mean weight of newborn infants at a community hospital is 6.6

pounds. A sample of seven infants is randomly selected and their weights at birth are

recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does the sample data show a

significant increase in the average birthrate at a 5% level of significance? (Points : 3)

Fail to reject the null hypothesis and conclude the mean is 6.6 pounds.

Reject the null hypothesis and conclude the mean is lower than 6.6 pounds.

Cannot calculate because the population standard deviation is unknown. Reject the null hypothesis and conclude the mean is greater than 6.6 pounds. Question 22.22. The coefficient of determination is the square root of the coefficient of

correlation. (Points : 3)

True

False Question 23.23. If the coefficient of correlation is 0.80, the coefficient of determination is

0.64. (Points : 3)

True

False Question 24.24. If the coefficient of determination is 0.94, what can we say about the

relationship between two variables? (Points : 3)

The direction of the relationship is positive.

94% of the total variation of the dependent variable is explained by the

independent variable.

The direction of the relationship is negative.

The strength of the relationship is 0.94. Question 25.25. For an inverse relationship between two variables, the sign of the

correlation coefficient is &quot;+&quot;. (Points : 3)

True

False Question 26.26. Which of the following statements regarding the coefficient of

correlation is true? (Points : 3)

It describes the relationship between two variables. It is calculated as the square of the slope.

A value of 0.00 indicates two variables are related.

It ranges from 0.0 to +1.0 inclusive. Question 27.27. The Pearson product-moment correlation coefficient, r,

requires that variables be measured with _____________. (Points : 3)

an ordinal or ratio scale

an interval or ratio scale

a nominal or ratio scale

a nominal or ordinal scale Question 28.28. The least squares technique minimizes the sum of the squares of the

vertical distances between the actual Y values and the predicted values of Y. (Points : 3)

True

False Question 29.29. What is the general form of the regression

equation? (Points : 3)

? = a + (bX)

? = abX

? = ab

? = (a + b)X Question 30.30. In the least squares equation, ? = 10 + 20X, the value of 20 indicates

____________. (Points : 3)

That Y increases by 20 units for each unit increase in X

That X increases by 20 units for each unit increase in Y The Y-intercept increases by 20 units for each unit increase in X

The error in prediction Question 31.31. Given the least squares regression equation, ? = 1,202 +

1,133X, when X = 3, what does ? equal? (Points : 3)

4,601

8,000

5,734

4,050 Question 32.32. Assume the least squares equation is ? = 10 + 20X. What does the

value of 10 in the equation indicate? (Points : 3)

Y increases by 10 for each unit increase in X

X increases by 10 for each unit increase in Y

It is the error of estimation.

When X = 0, Y = 10

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