Question

A claim is made that the average college student spends 85 minutes per day on social media. Casey believes this claimed value is too low. He surveys a random sample of 115 college students, and they report spending an average of 90 minutes per day on social media, with a sample standard deviation of 19.5 minutes. When Casey computed his test statistic, he did so as follows: 2 -2.7 85-90 19.5 V115 What is wrong with Casey's computations? Instead of subtracting 90 from 85 in the numerator, Casey should subtract 85 from 90. Casey is using the wrong test statistic formula altogether. Instead of dividing by the square root of 115 in the denominator, Casey should divide by the square root of 100. The denominator should be just 19.5, not 19.5 divided by the square root of 115. Nothing is wrong

Answer 1

What is wrong with Casey's computation?

Instead of subtracting 90 from 85 in the numerator, Casey should subtract 85 from 90.

Explanation

The equation of test statistic for the given case is,

T- 5 Vn

where,
T
is the sample mean. Here, $\bar{x}=90$

$\mu$ is the population mean. Here,

= 85

s is the sample standard deviation. Here, s=19.5

n is the sample size. Here, n=115

After substituting the values, the test statistic becomes,

$z=\frac{90-85}{\frac{19.5}{\sqrt{115}}}$

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