An IQ test was administered to twelve students and the scores were as follows:

Student

1

2

3

4

5

6

7

8

9

10

11

12

IQ score

87

102

94

81

115

75

74

116

98

114

96

100

Assume that IQ is normally distributed with mean m and variance .

1.If =196, construct a 95% confidence interval for m, the true mean IQ in the population.

(5 Marks)

2.What sample size is necessary to ensure an interval width w = 10? (5 Marks)

3.Now consider unknown. Is the claim that m is less than 100 justified? Perform a test at the a = 0.10 level of significance, by the following 5 steps:(10 Marks)

Step 1. Hypotheses and significance level:

H₀:H_a:a =

Step 2. Test Statistic and its sampling distribution under H₀:

Step 3. Observed value of the test statistic:

Step 4. P-value under H₀:

Step 5. Decision and conclusion (interpretation of the result):

Part II. (15 Marks)

In an initial drugs test, 5.8% of job applicants tested negative. It is claimed that now the rate is lower. A random sample of 1520 current job applicants ended in 58 negative results.

1.Construct a 95% confidence interval for p, the true proportion of negative results in the population (classical form). (5 Marks)

2.Conduct a statistical test of hypothesis on this claim at the 0.01 level of significance, by the same 5 steps as above. (10 Marks)