A simple random sample of 25 has been collected from a normally distributed population for which it is known that 17.0. The saMPLE MEAN HAS BEEN CALCULATED AS 342.0 AND THE sample standard deviation s=14.9. Construct and interpret the 95% and 99% confidence intervals for the population mean.

I don't know what the 17.0 signifies.

95% interval = mean ± 1.96 SEm (Standard Error of the mean)

SEm = SD/√(n-1)

99% interval = mean ± 2.575 SEm

To construct the confidence intervals for the population mean, we need to use the formula:

Confidence Interval = Sample Mean ± Margin of Error

The margin of error is calculated using the formula:

Margin of Error = Critical Value * (Standard Deviation / Square Root of Sample Size)

First, let's calculate the critical values corresponding to the desired confidence levels.

For a 95% confidence level, we need to find the critical value at the 2.5% percentile from the standard normal distribution (since it is a two-tailed test). Using a standard normal distribution table or a statistical calculator, we find the critical value to be approximately 1.96.

For a 99% confidence level, the critical value is approximately 2.57.

Now, let's calculate the confidence intervals for the population mean.

For the 95% confidence interval:

Margin of Error = 1.96 * (14.9 / sqrt(25))
= 1.96 * (14.9 / 5)
= 1.96 * 2.98
= 5.84

Lower Bound = Sample Mean - Margin of Error
= 342.0 - 5.84
= 336.16

Upper Bound = Sample Mean + Margin of Error
= 342.0 + 5.84
= 347.84

Therefore, the 95% confidence interval for the population mean is (336.16, 347.84). We can interpret this as, "We are 95% confident that the true population mean is between 336.16 and 347.84."

For the 99% confidence interval, we follow the same steps:

Margin of Error = 2.57 * (14.9 / sqrt(25))
= 2.57 * (14.9 / 5)
= 2.57 * 2.98
= 7.66

Lower Bound = Sample Mean - Margin of Error
= 342.0 - 7.66
= 334.34

Upper Bound = Sample Mean + Margin of Error
= 342.0 + 7.66
= 349.66

Therefore, the 99% confidence interval for the population mean is (334.34, 349.66). We can interpret this as, "We are 99% confident that the true population mean is between 334.34 and 349.66."

It's important to note that increasing the confidence level results in a wider interval as it allows for a greater level of uncertainty. Conversely, decreasing the confidence level would provide a narrower interval but with less confidence in capturing the true population mean.