Performing Hypothesis Testing
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Using a hypothesis test with a well known 4 step procedure, state your conclusion for the 0.05 significance level:
A. Based on responses from 1,015 randomly selected teens, which concluded that 44% of teens say grades are the greatest source of pressure, test the claim that fewer than half of all teens in the population feel that grades are the greatest source of pressure.
B. 276,000 students were asked about their attitudes on a variety of subjects. From a 2000 survey, 51% of second year students believe that abortion should be legal, down from 65% in 1985. Test the claim that over half of all second year students believe that abortion should be legal.
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A. Based on responses from 1,015 randomly selected teens, it was concluded that 44% of teens say grades are the greatest source of pressure. Test the claim that fewer than half of all teens in the population feel that grades are the greatest source of pressure.
Solution: We can set up the null and alternative hypotheses
- the null hypothesis H0: p=p*=50%
- the alternative hypothesis H1: p<50%
Now we have a sample with size n=1015 and get the sample mean of proportion of teens in the population feel that grades are ...
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- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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