Mathematics, 24.12.2019 19:31 daniiltemkin20

You are given the sample mean and the population standard deviation. use this information to construct the 90% and 95% confidence intervals for the population mean. interpret the results and compare the widths of the confidence intervals. if convenient, use technology to construct the confidence intervals.

Answers: 2

Show answers

Answers

Answer from: smagallanes

The 90% confidence interval would be given by (110.168;117.832)

The 95% confidence interval would be given by (119.393;118.607)

Step-by-step explanation:

Assuming this info:" A random sample of 45 home theater systems has a mean price of $114.00. Assume the population standard deviation is $15.30. Construct a 90% and 95 confidence interval for the population mean".

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=114$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=15.30 represent the sample standard deviation

n=45 represent the sample size

2) 90% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are given by:

df=n-1=45-1=44

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,44)".And we see that $t_{\alpha/2}=1.68$

Now we have everything in order to replace into formula (1):

$114-1.68\frac{15.30}{\sqrt{45}}=110.168$

$114+1.68\frac{15.30}{\sqrt{45}}=117.832$

So on this case the 90% confidence interval would be given by (110.168;117.832)

3) 95% confidence interval

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,44)".And we see that $t_{\alpha/2}=2.02$

Now we have everything in order to replace into formula (1):

$114-2.02\frac{15.30}{\sqrt{45}}=119.393$

$114+2.02\frac{15.30}{\sqrt{45}}=118.607$

So on this case the 95% confidence interval would be given by (119.393;118.607)

Answer from: Quest

What’s the question?
Max points i can ! it’s in math because i trust the math people more.

Answer from: Quest

Idon’t exactly understand but i think dbc=rst

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 19:30, vanessagallion

Evaluate 3(a + b + c)squared for a = 2, b = 3, and c = 4. a. 54 b. 243 c.729 add solution .

Answers: 1

continue

Mathematics, 21.06.2019 21:30, cassandramanuel

Carl's candies has determined that a candy bar measuring 3 inches long has a z-score of +1 and a candy bar measuring 3.75 inches long has a z-score of +2. what is the standard deviation of the length of candy bars produced at carl's candies?

Answers: 1

continue

Mathematics, 22.06.2019 00:30, angelthompson2018

Francisco's credit card has an apr of 28.98%, calculated on the previous monthly balance. his credit card record for the last 7 months is shown in the table below francisco is trying to figure out what this all means. answer the following questions: what is the total amount that francisco has paid in interest over the 7 months? what is the total amount that francisco has made in payments over the 7 months? how much of francisco's payments have gone to paying down the principal on his account? what is francisco's new balance at the end of month 8? what will francisco be charged for interest for month 8?

Answers: 2

continue

Mathematics, 22.06.2019 01:30, yennifervilleda05

The water aquarium shark tank is always greater than 25 feet of the water level decreased by 6 feet during cleaning what was the water level before the cleaners took out any water

Answers: 1

continue

You know the right answer?

You are given the sample mean and the population standard deviation. use this information to constru...