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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.

Respuesta :

SaniShahbaz

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:

[tex]M.E=z_{\frac{\alpha}{2} } \times \frac{\sigma}{\sqrt{n}}[/tex]

Here,

[tex]z_{\frac{\alpha}{2} }[/tex] 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.

[tex]\sigma[/tex] 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%.

The two recommendations should be that the sample size should be increased and the confidence interval should be reduced.

Suggestions for reducing the margin of error:

Since 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.

We know that margin of error = z value × population / √n

So for reducing the margin of error of the interval,  sample size should be increased and the confidence interval should be reduced.

Learn more about mean here: https://brainly.com/question/20875379

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