Given that barx 30 n 49 and sigma 3 then we can be 95...

Given that $\bar{x} = 30$, $n = 49$, and $\sigma = 3$, then we can be 95% confident that the true mean, $\mu$, lies between the values $\underline{\hspace{1cm}}$ and $\underline{\hspace{1cm}}$. Round your critical value to two decimal places. Round your final answers to two decimal places.

Transcript

00:01 Alright, so to calculate the 95 % confidence interval for the population mean, you can use the formula for confidence interval.

00:09 So, confidence interval equals sample mean plus or minus the critical value times the population standard deviation, divided by the square root of the sample size.

00:31 So, we would obviously change these into variables, but for now, let's just say the sample mean is x to the line over plus or minus the...

00:53 Actually, we'll just do that later.

00:56 But this is the formula with words, and the given values you have are the sample mean, which is just 30, the sample size, which is just 25, the population standard deviation, which is just 4, and the confidence level, which is just 85%.

01:18 And let's start with a.

01:22 So, for a, find the critical value.

01:24 So, since the confidence level is 75%, we need to find the critical value corresponding to the 95 % confidence level.

01:30 So, this critical value can be obtained from a z -table, a variety calculator, and for a 95 % confidence level, the critical z -value is approximately 1 .96.

01:48 Alright, now we're going to calculate the margin of error, the m -over -e, and the formula for this would be critical value times population.

02:01 Let's just say, sorry, same thing as before, psd, population standard deviation.

02:06 Population standard deviation divided by square root of sample size.

02:15 And with the information we have, it's just 1 .964 divided by square root of 25, and we just get approximately 1 .568...

Question

Given that $\bar{x} = 30$, $n = 49$, and $\sigma = 3$, then we can be 95% confident that the true mean, $\mu$, lies between the values $\underline{\hspace{1cm}}$ and $\underline{\hspace{1cm}}$. Round your critical value to two decimal places. Round your final answers to two decimal places.

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