A recent national survey found that high school students watched an average (mea

Question

A recent national survey found that high school students watched an average (mean) of 6.7 DVDs per month with a population standard deviation of .80. A random sample of 40 college students revealed that the mean number of DVDs watched last month was 6.20. At the .05 significance level, can we conclude that college students watch fewer DVDs a month than high school students?

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign.Round your answer to 2 decimal places.)

Explanation / Answer

The test statistic found here was z = -8.85437744847147 (approximately)

This is very very far from the center value of z = 0. In fact, it's more than 8 standard deviations away from the mean. So it's very unlikely to observe this value if it randomly came up (assuming the null is true). Usually, the most likely values will fall within 3 standard deviations (on either side). But this is more than 8 standard deviations away.
This means that the p-value is very small. So small that it's practically zero. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.
So we can conclude that college students watch fewer DVDs a month than high school students.

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