12. (13 Pts) IQ\'s measured on the Stanford Revision of the Binet-Simon Intellig

Question

12. (13 Pts) IQ's measured on the Stanford Revision of the Binet-Simon Intelligence Scale are supposed to have a standard deviation of 16 points. Twenty five randomly selected people were given the IQ test where the sample mean = 103.52 points and sample standard deviation = 15 points. At the 10% significance level, do the data provide sufficient evidence to claim that the standard deviation of IQ's measured on this scale is different than 16 points. Analysis of the data showed the Shapiro-Wilk normality test has a p-value = 0.8545. a) This problem is about (Circle your choice): One Population mean One population standard deviation One population proportion Two Population means - independent samples Two population means-paired samples b) Determine the null and alternate hypothesis for this problem. e) Check if the assumptions are met to test this hypothesis d) If the assumptions are met. show how you determine if the null hypothesis is rejected or not rejected, if the p-value = 0.7356. e) Write the interpretation

Explanation / Answer

a) One population SD

b) Null:   = 16

Alt: 16

c) Assumption: Normality assumption is there

Yes assumptions are satisfied as p value (0.8545) > alpha

d) p value for test = 0.7356

alpha = 0.01

p value > 0.01

So, null is not rejected

e) As null is not rejected we can conclude that IQs measured on scale have SD = 16 points

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