Question

In: Statistics and Probability

Here are the IQ test scores of a sample of 12 seventh-grade girls in a Midwestern...

Here are the IQ test scores of a sample of 12 seventh-grade girls in a Midwestern school district:

114

105

86

96

89

120

103

93

114

128

107

100

  1. What are the mean and standard deviation of these IQ scores?

  1. What proportion of the scores is within one standard deviation of the mean? What proportion of the scores is within two standard deviations of the mean?

  1. What would we expect the proportions in part (b) to be if the scores followed a Normal distribution?

  1. Is the true distribution of scores close to a Normal distribution or not? In your opinion, would it be reasonable to claim that IQ test scores follow a Normal distribution?

Solutions

Expert Solution

a) From the given data

b)


Related Solutions

) Scores on an IQ test are normally distributed. A sample of 20 IQ scores had...
) Scores on an IQ test are normally distributed. A sample of 20 IQ scores had standard deviation s = 8. The developer of the test claims that the population standard deviation is ı = 12. Do these data provide sufficient evidence to contradict this claim? Use the Į = 0.05 level of significance. 3) A) Reject H0. The population standard deviation appears to differ from 12. B) Do not reject H0. There is insufficient evidence to conclude that the...
Scores on an IQ test are normally distributed. A sample of 10 IQ scores had standard...
Scores on an IQ test are normally distributed. A sample of 10 IQ scores had standard deviation s=7. (a) Construct a 98% confidence interval for the population standard deviation . Round the answers to at least two decimal places. (b) The developer of the test claims that the population standard deviation is 9. Does this confidence interval contradict this claim? Explain  
(15pts) A researcher wants to compare IQ scores for boys and girls. He obtained IQ scores...
(15pts) A researcher wants to compare IQ scores for boys and girls. He obtained IQ scores for 47 randomly sampled seventh-grade boys in a Midwest school district and 31 seventh- grade girls in the same district. (a) Based on the design, which test should the researcher use to analyze the data? One-sample t test, matched-pair t test or two-sample t test?(2pts) (b) Based on the JMP output below, report the 95% CI for the mean IQ score difference between boys...
Jennifer falls in the 98th% in her Stanford-Binet IQ test scores at age 12. Discuss:   ...
Jennifer falls in the 98th% in her Stanford-Binet IQ test scores at age 12. Discuss:    1. What her score would actually be and how it’s computed, including her MA.    2. Whether this test can be a good or bad predictor of the child’s future          success in school and work.       3. What aspects of intelligence Sternberg and Gardner would argue are critical           in determining intelligence and are not measured by the Stanford-Binet test.
A random sample of 83 eighth grade​ students' scores on a national mathematics assessment test has...
A random sample of 83 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 278. This test result prompts a state school administrator to declare that the mean score for the​ state's eighth-graders on this test is more than 275. Assume that the population standard deviation is 35. At α=0.08 is there enough evidence to support the​ administration's claim? Complete parts​ (a) through​ (e). A is done B: fine the standardized test statistic z,...
A random sample of 80 eighth grade​ students' scores on a national mathematics assessment test paper...
A random sample of 80 eighth grade​ students' scores on a national mathematics assessment test paper has a mean score of 269. This test result prompts a state school administrator to declare that the mean score for the​ state's eighth graders on this paper is more than 260 Assume that the population standard deviation is 31. At alphaαequals=0.06 is there enough evidence to support the​ administrator's claim? Complete parts​ (a) through​ (e). ​(a) Write the claim mathematically and identify Upper...
A random sample of 77 eighth-grade​ students' scores on a national mathematics assessment test has a...
A random sample of 77 eighth-grade​ students' scores on a national mathematics assessment test has a mean score of 264 with a standard deviation of 40. This test result prompts a state school administrator to declare that the mean score for the​ state's eighth-graders on this exam is more than 260. At a=0.09​, is there enough evidence to support the​ administration's claim? Complete parts​ (a) through​ (e).
An IQ test has scores converted to Z scores. What % of people fall below a...
An IQ test has scores converted to Z scores. What % of people fall below a z = -2? Group of answer choices 2.28% 47.7% 97.7% 2%
. It is known that scores on a certain IQ test follow a normal distribution with...
. It is known that scores on a certain IQ test follow a normal distribution with mean 100 and standard deviation 15. For the whole population of test-takers, what proportion of scores will be greater than 124.0? Also, the top 3% of test-takers will have scores greater than what value? Finally, consider a random group of 16 people who take the IQ test. For these 16 people, what is the probability that their average (mean) IQ score will be less...
Sarah scores an 85 on an (IQ) test with a mean of 94 and a standard...
Sarah scores an 85 on an (IQ) test with a mean of 94 and a standard deviation of 10. At what percentile rank is she with respect to the rest of the population? Please show work- thank you.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT