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Most sod distributors claim that sod has to be watered twice a day for at least...

Most sod distributors claim that sod has to be watered twice a day for at least 8 days in order to adhere to its new environment. A researcher takes a random sample of 75 patches of sod and waters them until the root base adheres to the ground. The average number of days it took for the roots to adhere to the ground was 9.9 days. Assume that the population standard deviation σ is 2.3 days.

What is the point estimate for the mean number of days it takes sod to root?

What is the margin of error for a 99% confidence interval for the mean number of days it takes sod to root? Round to 3 decimal places.

What is the upper bound for the 99% confidence interval for the mean number of days it takes sod to root? Round to 3 decimal places.

Suppose that the standard deviation given was actually the sample standard deviation, s. What is the lower bound for the 99% confidence interval for the mean number of days it takes sod to root? Round to 3 decimal places.

Math   Statistics-And-Probability   
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Answer #1

Point estimate of mean is

As population standard deviation is known, so we will use z distribution to find Margin of Error

For 99% CI, z value is 2.576 as P(-2.576<z<2.576)=0.99

So Margin of Error is

Hence CI is

Hence the upper bound for the 99% confidence interval for the mean number of days it takes sod to root is 10.584

Even if we take sample standard deviation, we will use t distribution

And value of t for 99% CI is TINV(0.01,74)=2.644

So Margin of Error is

Hence CI is

Hence the lower bound for the 99% confidence interval for the mean number of days it takes sod to root is 9.198

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