The IQ scores from Question 2 are 114 100 104 89 102 91 114 114 103 105 108 130
ID: 3065185 • Letter: T
Question
The IQ scores from Question 2 are
114
100
104
89
102
91
114
114
103
105
108
130
120
132
111
128
118
119
86
72
111
103
74
112
107
103
98
96
112
112
93
114
100
104
89
102
91
114
114
103
105
108
130
120
132
111
128
118
119
86
72
111
103
74
112
107
103
98
96
112
112
93
4. (15 points) The mean IQ for the entire population in any age group is supposed to be 100. Treat the IQ scores in Question 2 above as if they were an SRS (simple random sample) from all middle-school girls in this district. Do the scores provide good evidence that the mean IQ of this population is not 100? Go through steps a - c below to figure this out (a) What is the null hypothesis and the alternative hypothesis? (b) Compute the z-score and the p-value. (c) Interpret your results: i) Do you reject your null hypothesis? ii) Are your results statistically significant at the iii) What does the p-value mean? 0.025 level?Explanation / Answer
a)
Hypothesis:
Null hypothesis: mu = 100
Alternative hypothesis: mu not equal to 100
b)
x = 105.84 , s = 14.2714
z = ( x - mean) /(s/sqrt(n))
= ( 105.84 - 100)/(14.2714/sqrt(31))
= 2.2784
p value is calculated using z = 2.2784 at 0.025 significance level
p value = 0.0227
c)
we rejct the null hypothesis
Results are significant at the alpha =0.025 level
The P value, or calculated probability, is the probability of finding the observed, or more extreme, results when the null hypothesis (H0) of a study question is true – the definition of ‘extreme’ depends on how the hypothesis is being tested.
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