Question

Twenty-five students were randomly selected and asked "How many hours of TV did you watch this weekend?" The sample mean for the data is 5 hours.
The dotplot below shows the distribution of the sample mean hours of TV watched for 500 random samples of size 25 taken with replacement from the
original sample.
45
6
S.S
Simulated sample mean
Distribution of Simulated Mean
• samples mean SD
500 4.969 0.288
Use the results of the simulation to approximate the margin of error for the estimate of the mean number of hours of television watched. (answer in the
format 0.123)

Answer 1

Using a confidence level of 95%, the margin of error for the estimate of the mean number of television hours watched will be 1.129

The approximate margin of error can be calculated using the relation :

• Margin of Error = $Z_{\frac{α}{2}} \frac{σ}{\sqrt{n}}$

• Sample size, n = 25
• Standard deviation, = 2.88
• Confidence level = 95%

• $Z_{\frac{α}{2}} = 1.96$

Margin of Error = $1.96 \frac{2.88}{\sqrt{25}}$

Margin of Error = $1.96 \frac{2.88}{5}$

Margin of Error = $1.96 \times 0.576$

Margin of Error = $1.129$

Therefore, the margin of error for the estimate of the mean number of television hours watched is 1.129.

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