A standardized third grade reading test, called the We Can Read Test, has a mean of 50 with a standard deviation of 10. A developmental psychologist conducts a study, where he assesses the reading ability of a random sample of 75 third graders using the We Can Read Test, and finds a mean of 53 with a standard deviation of 12.
11. Which of the following is a statistic?
a. 50
b. 53
c. 75
d. 10
12. Which of the following is a parameter?
a. 75
b. 53
c. 10
d. 12
13. What is the measure of spread of the sampling distribution of sample means?
a. 10
b. 12
c. 1.15
d. 1.39
14. What proportion of a normal distribution corresponds to z scores greater than +1.23? a. .8907
b. .3907
c. .6093
d. .1093
15. What is the percentage of observations that fall between az score of -2.3 and +0.70?
a. 74.73
b. 25.80
c. 48.93
d. 75.80
11, 12. A statistic is a measure on a sample, while a parameter is a measure on a population.
13. SEm = SD/√n = SEm = 12/√75 = ?
14, 15. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores.
11. The correct answer is b. 53. In statistics, a statistic is a numerical characteristic that describes a sample, such as the mean or standard deviation. In this case, the mean of 53 is a statistic because it describes the sample of 75 third graders who took the test.
To get the answer, you need to understand the definition of a statistic and identify which of the options is a value that describes a sample.
12. The correct answer is a. 75. In statistics, a parameter is a numerical characteristic that describes a population, such as the population mean or standard deviation. In this case, the number 75 is a parameter because it describes the population of all third graders who could potentially take the test.
To get the answer, you need to understand the definition of a parameter and identify which of the options is a value that describes a population.
13. The correct answer is c. 1.15. The measure of spread of the sampling distribution of sample means is called the standard error. To calculate the standard error, you divide the standard deviation of the population by the square root of the sample size.
In this case, the standard deviation of the population is given as 10, and the sample size is 75. Therefore, to calculate the standard error, you divide 10 by the square root of 75.
To get the answer, you need to know the formula for calculating the standard error and perform the calculation using the given values.
14. The correct answer is c. 0.3907. To find the proportion of a normal distribution that corresponds to z scores greater than a certain value, you can use a standard normal distribution table (also known as a z-table) or a calculator that can compute normal distribution probabilities.
In this case, the z-score is +1.23. Using a z-table or a calculator, you can find the proportion (or probability) of a normal distribution that corresponds to this z-score.
To get the answer, you need to use a z-table or a calculator to find the proportion that corresponds to the given z-score.
15. The correct answer is b. 25.80. To find the percentage of observations that fall between two z-scores, you can use a standard normal distribution table (z-table) or a calculator that can compute normal distribution probabilities.
In this case, the z-scores are -2.3 and +0.70. Using a z-table or a calculator, you can find the proportion (or probability) of a normal distribution that corresponds to each of these z-scores. Then, subtract the smaller proportion from the larger proportion and multiply by 100 to convert it to a percentage.
To get the answer, you need to use a z-table or a calculator to find the proportions that correspond to the given z-scores, subtract the smaller proportion from the larger proportion, and multiply by 100 to convert it to a percentage.