A psychologist has developed a standardized test for measuring vocabulary skills

Question

A psychologist has developed a standardized test for measuring vocabulary skills for 4 - year - old children. The scores on the test form a normal distribution with mu = 70 and sigma_x = 20. A researcher would like to use the test to investigate the hypothesis that children. who grown up researcher would like to use the test to investigate the hypothesis that children who grown up as a only child develop vocabulary skills at a faster rate than children in large families. A sample of n = 25 only children is obtained and the mean test score for the sample is 77. Is this sample sufficient to conclude that vocabulary skills for only children are significantly higher than those for the general population Use a one - tailed test with alpha set at.05. Is this sample sufficient to conclude that vocabulary skills for only children are significantly different from those for the general population Use a two - tailed test with alpha =.05.

Explanation / Answer

a) Population standard deviation is known, use 1-sample Z test to test the claim usisng one-talied alternative hypothesis.

Z=(Xbar-mu)/(sigma/sqrt N), where Xbar is sample mean, mu is population mean and sigma is population standard deviation , N is sample size.

=(77-70)/(20/sqrt 25)

=1.75

P value is 0.0000. P value is less than aalpha=0.05. Reject null hypothesis to conclude that vocabulaary skills for only children are significantly higher than thse for general population.

b) P value for two-tailed test is 0.0000. The p value is less than alpha=0.05. Therefore, reject null hypothesis to support the claim.

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