4)
Assume that IQ scores of college graduates are normally distributed. A researcher collects a random sample of 25 college graduates and tests their IQ. The sample had a mean IQ of 108 with a standard deviation of 15.6.
a) Find a 95% confidence interval for the true mean IQ for college graduates.
b) Provide the margin of error of the interval as your answer.
Round your answer to 1 decimal place.
Solution :
Given that,
Point estimate = sample mean = = 108
sample standard deviation = s = 15.6
sample size = n = 25
Degrees of freedom = df = n - 1 = 25 - 1 = 24
At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
t /2,df = t0.025,24 = 2.064
Margin of error = E = t/2,df * (s /n)
= 2.064 * (15.6 / 25)
= 6.4
The 95% confidence interval estimate of the population mean is,
- E < < + E
108 - 6.4 < < 108 + 6.4
101.6 < < 114.4
(101.6 , 114.4)
4) Assume that IQ scores of college graduates are normally distributed. A researcher collects a random...
The IQ scores of college students are normally distributed with the mean of 120 and standard deviation of 10. If a random sample of 25 students is taken, what is the probability that the mean of this sample will be between 120 and 125. (49.38%)
Assume that IQ scores are normally distributed, with a standard deviation of 12 points and a mean of 100 points. If 50 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points? (Round your answer to four decimal places.)
The IQ scores of adults are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that the mean IQ score in a random sample of 50 adults will be more than 95?
Suppose the preliteracy scores of three-year-old students in the United States are normally distributed. Shelia, a preschool teacher, wants to estimate the mean score on preliteracy tests for the population of three-year-olds. She draws a simple random sample of 20 students from her class of three-year-olds and records their preliteracy scores (in points). 74, 79, 83, 85, 88, 90, 94, 95, 95, 97,99, 99, 100, 103, 105, 105, 106, 107, 107, 108 Click to download the data in your preferred...
Suppose the preliteracy scores of three-year-old students in the United States are normally distributed. Shelia, a preschool teacher, wants to estimate the mean score on preliteracy tests for the population of three-year-olds. She draws a simple random sample of 20 students from her class of three-year-olds and records their preliteracy scores (in points) 74,79,83,85, 88, 90, 94,95, 95,97,99,99, 100, 103, 105, 105,106, 107, 107, 108 Click to download the data in your preferred format. CrunchIt! CSV Excel JMP Mac Text...
Intelligence quotient (IQ) scores are often reported to be normally distributed with a mean of 100 and a standard deviation of 15. (a) If a random sample of 50 people is taken, what is the probability that their mean IQ score will be less than 95? (b) If a random sample of 50 people is taken, what is the probability that their mean IQ score will be more than 95? (c) If a random sample of 50 people is taken,...
For randomly selected adults, IQ scores are normally distributed with a standard deviation of 15. For a simple random sample of 25 randomly selected college students, their IQ scores have a standard deviation of 18. Use a 5% level of significance; test the claim that the IQ scores of college students are less consistent (higher standard deviation) compare to the IQ scores of the general population.
1. Scores on an IQ test for the 18-to-30 age group are approximately normally distributed with a mean of 110 and a standard deviation 25. Scores for the 31-to-40 age group are approximately normally distributed with mean 100 and standard deviation 20. Phoebe, who is 25, scores 130 on the test. Amandeep, who is 36, also takes the test and scores 116. Who scored higher relative to her age group, Phoebe or Amandeep? a) Phoebe b) Amandeep c) They scored...
Suppose a psychologist specializing in learning disorders wanted to estimate the mean IQ score for children with a particular type of learning disorder. She obtained a random sample of 10 children with this learning disorder and recorded the following IQ scores. 105,96,102,95,91,98,109,122,88,129 IQ scores in the general population are normally distributed with a mean of 100.0 points and a standard deviation of 15.0 points. The psychologist was willing to assume that the distribution of IQ scores for all children with...
Suppose a random sample of size 17 was taken from a normally distributed population, and the sample standard deviation was calculated to be s = 5.0. a) Calculate the margin of error for a 95% confidence interval for the population mean. Round your response to at least 3 decimal places. b) Calculate the margin of error for a 90% confidence interval for the population mean. Round your response to at least 3 decimal places.