statistic

posted by .

1. Past experience indicates that the variance, ¦Ò2x, of the scores, X, obtained on the verbal portion of a test is 5,625. Similarly, the variance ¦Ò2y, of the scores, Y, on the mathematical portion is 2,500.
(a) A random sample of size n = 64 yields a sample mean verbal score of 600. Find a 95% confidence interval on the true average score obtained on the verbal aptitude test.
(b) A random sample of size n = 80 yields a sample mean mathematics score of 500. Find a 95% confidence interval on the true average score obtained on the mathematical aptitude test.
(c) Find a 90% confidence interval on ¦Ìy based on the data from (b). Compare the two (95% and 90%) intervals obtained. What does this result imply about the relationship between interval length and degree of confidence?
(d) Ten years prior to the year in which the above data were obtained, ¦Ìy was found to be 520. Can we safely conclude that the average score has declined over the past 10 years? Explain your answer briefly, on the basis of the confidence intervals constructed in (b) and (c)

  • statistic -

    (a) and (b) Variance = SD^2

    95% = mean ± 1.96 SEm

    SEm = SD/√(n-1)

    (c) 90% = mean ± 1.645 SEm

    (d) Z = (mean1 - mean2)/standard error (SE) of difference between means

    SEdiff = √(SEmean1^2 + SEmean2^2)

    SEm = SD/√(n-1)

    If only one SD is provided, you can use just that to determine SEdiff.

    Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.

    I leave the calculations to you.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. statistics

    A researcher is testing a null hypothesis that states: H: ì = 50. A sample of 25 scores is selected and the mean is M = 55.Assuming that the sample variance is s2 = 100, compute the estimated standard error and the t statistic. Is …
  2. statistics

    A psychologist wants to estimate the variance of employee test scores. A random sample of 18 scores had a sample standard deviation 10.4. Find a 90% confidence 2 interval for the population variance. What assumption, if any, have you …
  3. statistics

    The box plot below summarize the distributions of SAT verbal and math scores among students at an upstate New York high school. 300 400 500 600 700 800 data Whic of the following statements is false?
  4. Statistics

    The Education Testing Service conducted a study to investigate differences between the scores of males and females on the SAT. The study identified a random sample of 562 females and 852 males that had achieved the same high score …
  5. statistic/Psychology

    According to classical test theory, if the observed variance of a test is 50 and the true variance is 40, what is the estimated reliability of the test?
  6. statistic/Psychology

    According to classical test theory if the observed variance of a test is 50 and the true variance is 40 what is the estimated reliability of the test?
  7. statistics

    Suppose that on a certain examination in advanced mathematics, students from University A achieve scores which are normally distributed with a mean of 625 and a variance of 100, and that students from University B achieve scores which …
  8. math

    Test scores on a university admissions test are normally distributed, with a mean of 500 and a standard deviation of 100. a. What is the probability that a randomly selected applicant scores between 425 and 575?
  9. Stats (Math)

    Assume that Science scores on a 25-point quiz for a random sample of 5 students were drawn from a normal population. The assumed variance was 20 while the recorded variances were: 18, 16, 10, 13, and 23. You suspected that the variance …
  10. Statistics

    A sample of n = 25 scores has a mean of M = 40 and a variance of s2 = 100. If this sample is being used to test a null hypothesis stating that m = 43, then what is the t statistic for the sample

More Similar Questions