Question

In a survey conducted by the Gallup​ Organization, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the​ results, a​ 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5. Provide two recommendations for decreasing the margin of error of the interval.

Answer 1

Answer:

1) Increase the sample size

2) Decrease the confidence level

Step-by-step explanation:

The 95% confidence interval built for a sample size of 1100 adult Americans on how much they worked in previous week is:

42.7 to 44.5

We have to provide 2 recommendations on how to decrease the margin of Error. Margin of error is calculated as:

$M.E=z_{\frac{\alpha}{2} } \times \frac{\sigma}{\sqrt{n}}$

Here,

$z_{\frac{\alpha}{2} }$ is the critical z-value which depends on the confidence level. Higher the confidence level, higher will be the value of critical z and vice versa.

$\sigma$ is the population standard deviation, which will be a constant term and n is the sample size. Since n is in the denominator, increasing the value of n will decrease the value of Margin of Error.

Therefore, the 2 recommendations to decrease the Margin of error for the given case are:

1. Increase the sample size and make it more than 1100
2. Decrease the confidence level and make it lesser than 95%.