In a recent study, Lepp, Barkley, and Karpinski (2014) reported that undergraduate students spend an average of 278.67 (standard error of the mean = 9.79) minutes per day using their cell phones. You may wonder whether cell phone usage at your university differs significantly from Lepp, Barkley, and Karpinski’s (2014) findings. Suppose a recent survey of students at your university found that students spend 255 minutes per day using their cell phones. Note that standard error of the mean and standard deviation are not the same thing. Standard error is a measurement on the sampling distribution; we calculate it using the standard deviation of the data as well as the number of samples collected:
In our example of cell phone data, what would our two-sided p-value be if the sample standard deviation was 60.2 (to 7 decimal places)?
Given the sample mean sample standard deviation .
The two sided confidence interval for mean based on the sample data is
The hypotheses are
The test statistic is . Here is the standard error of the mean.
The two-sided p-value is
If P-value , we reject the null hypothesis.
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