Question
Number 2 please !!!!!! 1. A researcher decides to look at IQ scores and wants to...
Number 2 please !!!!!!
1. A researcher decides to look at IQ scores and wants to know the probability of obtaining several individual scores. The population mean is 100 and the population standard deviation is 15. Determine the probability of obtaining a score above 125. Determine the probability of obtaining a score below 70. Determine the probability of obtaining a score between 95 and 105. 2. The same researcher decides to collect a sample of IQ scores from students in his class. He obtains the following scores from a sample: 97, 86, 75, 102, 110, 96, 120, 118, 114, 88, 79. Using the information from the previous question and this question, determine the probability of obtaining a sample with this mean. Determine if you should reject the null hypothesis at the p=.05, p=.01 and p=.001 levels. Use a two-tailed test. If statistically significant, determine the effect sizes using the appropriate equation for the problem (Cohen's d).
Answers
SOLUTION 2:(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho: μ=100
Ha: μ≠100
This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.
Test Statistics
The z-statistic is computed as follows:
Decision about the null hypothesis Using the P-value approach: The p-value is p=0.7636, and since p = 0.7636 \ge 0.05p=0.7636≥0.05, it is concluded that the null hypothesis is not rejected.
(5) Conclusion: It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is different than 100, at the 0.05,0.1 and 0.001 significance level.
The result is NOT SIGNIFICANT.
EFFECT SIZE=
SMALL
X - MO 0/n 98.64 - 100 - 15/ 11 = -0.301T-ulo = 98.64 – 100/15 = 0.091
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