In a random sample of 26 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a standard deviat

Question

In a random sample of 26 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a standard deviation of 0.23 pounds. Determine the 80% confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

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Thành Công 5 years 2021-08-06T01:43:01+00:00 1 Answers 30 views 0

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  1. Maris
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    2021-08-06T01:44:53+00:00
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    Answer:

    The critical value that should be used in constructing the confidence interval is T = 1.316.

    The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

    Step-by-step explanation:

    We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

    The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

    df = 26 – 1 = 25

    80% confidence interval

    Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.8}{2} = 0.9. So we have T = 1.316

    The critical value that should be used in constructing the confidence interval is T = 1.316.

    The margin of error is:

    M = T\frac{s}{\sqrt{n}} = 1.316\frac{0.23}{\sqrt{26}} = 0.059

    In which s is the standard deviation of the sample and n is the size of the sample.

    The lower end of the interval is the sample mean subtracted by M. So it is 2.8 – 0.059 = 2.741 pounds

    The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.059 = 2.859 pounds.

    The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

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