In this study, two questions were asked:
Q1. The mean verbal SAT score of all the students in this university is 580. Is this also the case for all stat students at this university? Note that verbal SAT scores in the U.S. have a standard deviation of 111.
Q2. Based on a recent study, roughly 80% of college students in the U.S. own a cell phone. Do the data provide evidence that the proportion of students who own cell phones in this university is lower than the national figure?
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Summary statistics:
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Our null value is the mean of the SAT verbal score at a university which is 580. The alternative is saying that the mean is not 580. In this graph, we can see that the SAT scores distribution is pretty symmetric. In the table, we can see that the scores have a mean of about 597 and a standard deviation of about 78.
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Hypothesis test results:
μ : mean of Variable H0 : μ = 580 HA : μ ≠ 580 Std. Dev. = 111
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The table above shows us that the mean verbal SAT score for the stat students is about 597 which is much higher than the rest of the school which is thought to be 580. Seing that out p-value is much lower than our alpha, our null value (Ho) was rejected and the difference between the each of the means is significant.
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95% confidence interval results:
μ : mean of Variable Std. Dev. = 111
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In the table above, we can see that there is a 95% chance that the verbal SAT score is between 584 and 610 which makes it very unlikely that it is 580.
Conclusion for Question 1:
These results were very different from what we expected. After finding the mean of our sample of stat students, we found that their mean score of 597 was much higher than our expected mean of 580. The formal statistical test produced a p-value of .011, which means that the data provides sufficient evidence to reject our null value (Ho) and to conclude that our stat stutents' mean is much different than the entire student bodies' mean. We are 95% confident that the mean SAT score is between 584 and 610.
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Our null value (Ho) is that the proportion of college students who own cell phones is .8 and the alternative (Ha) is the proportion is less than .8. In the graph above, we can see that about 78% of students in the stat classes own cell phones while about 22% don't have cell phones.
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Hypothesis test results:
Outcomes in : Cell Success : yes p : proportion of successes H0 : p = 0.8 HA : p < 0.8
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In the table, we can see that about 78% of students in our sample study own cell phones which is a little bit less than our national average of 80%. But seeing that our p-value is greater than alpha, there is not enough evidence to reject our null (Ho).
Conclusion for Question 2:
These results were basically what we expected. Although 78% is less than our expected 80%, there just isn't enough evidence to conclude that the proportion of students at this university who own a cell phone is less than our nationsl average of .8.
