Question

Test of Significance should include all of the following:

-Null and alternative hypothesis stated

-Level of significance stated, graph draw with critical region shaded and critical value indicated. (This is related to the lever of significance testing)

-Appropriate descriptive statistics of data.

-Test statistics (include formula)

-test statistic marked on graph

-Decision based on p-value.

-Non-technical sentence of conclusion and summary.

Part 1

Intelligence and the IQ test:

A persons IQ was initially defined as follows: Mental age/chronological age *100

Thus an IQ of 100 implies one's mental age is in agreement with one's actual age in years so such a person is very normal and of average intelligence. A 10-year old with an IQ of 130 has the intelligence level of a typical 13-year old. Over the years, researchers in education and psychology have debated the issues associated with the accurate determination and interpretation of a person's IQ. One of the earliers accepted standards was the Stanford-Binet IQ test which arose from work by the French psychologist Alfred Binet later modeffied by psychologists at Stanford University. In the mid-twentieth century, the Wechsler Adult Intelligence Scale (WAIS) developed by David Wechsler, was introduced and is favored today. At the Data and Story Library site. (htt://lib.stat.cmu.edu/DASL/) you will find a summary of an experiment designed to study the correlation (if any) between brain size and IQ. We are not interested in the correlation experiment inself but the associated data file provides a set of Wechsler IQ scores that you will work with in the exercises. Visit the DASL site, locate the data file for this experiment, and be sure you understand the meaning of the individual data point continuing to the exercises.

#1. Wechsler IQ scores for adults typically follow a distribution with mean 100 and standard deviation 15. Using the Full Scale IQ scores for females. Test the hypothesis that the mean of Female IQ scores is less than 115. Use a 0.05 level of significance.

Answer 1

Given that: - x ^- = 100 sigma = 15 let x be wecheler IQ scores for adults d = 0.05 n = 100 To test the hypothesis i.e null & Alternative hypothesis, H_0: mu = 115 H_0: mu < 115 The central region is Z_alpha = z_0.05 = 1.645 level of significance is 0.05 Test statistics, Z = x ^- mu/sigma/ squareroot n = 100 - 115/15/ squareroot 700 = -15/1.5 = -10 P_value = 0.00007 times 10 ^-19 < alpha = 0.05 \r\n p values is less than alpha we reject H_0 nat 5 % level of significance we may concluded that mean of female IQ score is less than 115