Question

A random sample of size n_(1)=27, taken from a normal population with a standard deviation sigma _(1)=5, has a mean ar{x} _(1)=76. A second random sample of size n_(2)=36, taken from a different normal population with a standard deviation sigma _(2)=4, has a mean ar{x} _(2)=38. Find a 98% confidence interval for mu _(1)-mu _(2). Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The confidence interval is ,<mu _(1)-mu _(2)< (Round to one decimal place as needed.)N K n=36,taken from a different normal population with a standard deviation =4,has a mean 2=38.Find a 98% confidence interval for -2 Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The confidence interval is<- (Round to one decimal place as needed.)

          A random sample of size n_(1)=27, taken from a normal population with a standard deviation sigma _(1)=5, has a mean ar{x} _(1)=76. A second random sample of size n_(2)=36, taken from a different normal population with a standard deviation sigma _(2)=4, has a mean ar{x} _(2)=38. Find a 98% confidence interval for mu _(1)-mu _(2).
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
The confidence interval is ,<mu _(1)-mu _(2)<
(Round to one decimal place as needed.)N
K
n=36,taken from a different normal population with a standard deviation =4,has a mean 2=38.Find a 98% confidence interval for -2 Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table.
The confidence interval is<- (Round to one decimal place as needed.)

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a random sample of size n127 taken from a normal population with a standard deviation sigma 15 has a mean barx 176 a second random sample of size n236 taken from a different normal popul 37344

Added by Roger B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Jen H

06/01/2023

Step 1

The standard error (SE) is calculated using the formula: SE = sqrt[(σ1^2 / n1) + (σ2^2 / n2)] where σ1 and σ2 are the standard deviations of the two populations, and n1 and n2 are the sample sizes. Plugging in the given values: SE = sqrt[(5^2 / 27) + (4^2 / Show more…

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A random sample of size n_(1)=27, taken from a normal population with a standard deviation sigma _(1)=5, has a mean ar{x} _(1)=76. A second random sample of size n_(2)=36, taken from a different normal population with a standard deviation sigma _(2)=4, has a mean ar{x} _(2)=38. Find a 98% confidence interval for mu _(1)-mu _(2). Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The confidence interval is ,<mu _(1)-mu _(2)< (Round to one decimal place as needed.)N K n=36,taken from a different normal population with a standard deviation =4,has a mean 2=38.Find a 98% confidence interval for -2 Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The confidence interval is<- (Round to one decimal place as needed.)

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00:01 We have a random variable that has a normal distribution with an unknown mean and a standard deviation of 12.

00:14 We're going to take a random sample size, random sample of size 36, and we're going to find a sample mean of 98.

00:29 We're going to compute a 95 % confidence interval for the population mean.

00:38 The confidence interval formula is going to be the following.

00:42 The sample mean plus, and because this is normal distribution, i'm going to use a z, times the standard deviation over square root of n.

01:01 That's going to be 98 plus, and okay, so it looks like this is broken into parts.

01:15 The critical value z star, this comes from the 95 % confidence part.

01:23 We have an alpha of 0 .05.

01:26 These are commonly known values.

01:30 You don't come up with them on your own.

01:33 They're going to be on a z chart, on a table, or in your calculator, but they're just commonly known values, so you just need to look it up.

01:41 The critical value for a 95 % confidence interval is 1 .96.

01:47 I'm going to be plugging that in here.

01:49 Standard deviation is 12 over square root 36.

01:57 Let's see, the margin of error part, that is just this part of the confidence interval.

02:15 It's like, how much is it going to deviate from the standard, sorry, from the sample mean? let's calculate that...

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