Answer to Question #197799 in Statistics and Probability for Jean Claude

Question

Question 1 (a). In each of the following research situations, state the type of statistical test that may be used to answer the research question. Give a brief reason for your answer.

 (ii). “As far as intelligence is concerned, women do not differ from the general population”. This is a claim by some researchers on gender issues. To test this claim, 100 women were sampled from the general population and their intelligence (IQ) measured. It was found that the mean IQ of the female sample was equal to 110. Assuming that the mean IQ in the general population is equal to 105 with a standard deviation of 10, how true is the claim by the researchers?

Answer 1

(i) One-Sample t Test

The one-sample t test is used to compare a sample mean (M) with a hypothetical population mean (μ0) that provides some interesting standard of comparison. The null hypothesis is that the mean for the population (µ) is equal to the hypothetical population mean: μ = μ0. The alternative hypothesis is that the mean for the population is different from the hypothetical population mean: μ ≠ μ0. To decide between these two hypotheses, we need to find the probability of obtaining the sample mean (or one more extreme) if the null hypothesis were true. But finding this p value requires first computing a test statistic called t.

(ii) $n=100,x=110, \mu=105,\sigma=10$

Let Null Hypothesis,

$H_o:$ Claim is true that women do not differ from the general population.

and Claim$H_a:$ is false.

Test-statistics-

$z=\dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$=\dfrac{110-105}{\frac{10}{\sqrt{100}}}\\[9pt]=\dfrac{5}{1}=5$

The standard value of statistics at 5% level of significance is 1.6449.

As Calculated value is greater than the Standard value. So we reject null hypothesis. i.e. Claim is false that Women do not differ from the general population.