IQ scores among the general population have a mean of 100 and a standard deviation of 15. A research

albusgks

albusgks

Answered question

2022-04-24

IQ scores among the general population have a mean of 100 and a standard deviation of 15. A researcher claims that the standard deviation, o, of IQ scores for males is less than 15. A random sample of 19 IQ scores for males had a mean of 101 and a standard deviation of 10. Assuming that IQ scores for males are approximately normally distributed, is there significant evidence (at the 0.05 level of significance) to conclude that the researcher's claim is correct?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.)
(a) State the null hypothesis H0, and the alternative hypothesis H1,
H0:
H1:
(b) Determine the type of test statistic to use.
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the critical value. (Round to three or more decimal places.)
(e) Can we support the claim that the standard deviation of IQ scores for males is less than 15?
a. Yes
b. No

Answer & Explanation

Barbara Navarro

Barbara Navarro

Beginner2022-04-25Added 18 answers

The chi-square test for variance is a non-parametric statistical procedure with a chi-square-distributed test statistic that is used for determining whether the variance of a variable obtained from a particular sample has the same size as the known population variance of the same variables.
Given data is appropriate for testing of hypothesis to test chi-square for single variance. Because it is a small sample test.
a) Null Hypothesis: H0:σ=15
Alternative Hypothesis H1:σ>15
Level of significance=5%
b) The type of test statistic is chi-square test for single variance
c) Test statistic
χ2=(n1)s2σ2
=(191)102152
=18×100225
=8
d) Critical value
Read the chi square table value at 5% level of significance for right tailed test at 18 degrees of freedom is
χ{tab}2=9.390
e) Yes the claim the standard deviation of IQ scores for males is less than 15.

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