April 28th Khan Unit

Layla is working on a PhD in computer science and wonders what the average page length is for dissertations in her field.

all three

What is the critical value t∗t∗t, start superscript, times, end superscript for constructing a 99%99%99, percent confidence interval for a mean with 111111 degrees of freedom?

2.576

What is the critical value t∗t∗t, start superscript, times, end superscript for constructing a 90%90%90, percent confidence interval for a mean with 666 degrees of freedom?

1.943

What is the critical value t∗t∗t, start superscript, times, end superscript for constructing a 95%95%95, percent confidence interval for a mean from a sample size of n=20n=20n, equals, 20 observations?

2.093

What is the critical value t∗t∗t, start superscript, times, end superscript for constructing a 95%95%95, percent confidence interval for a mean with 888 degrees of freedom?

2.306

Della has over 500500500 songs on her mobile phone, and she wants to estimate what proportion of the songs are by a female artist.

0.40±2.576500.40(0.60)​​

Problem A company wanted to estimate the mean lifetime of its new model of lightbulbs. They use a method for testing bulbs that accelerates the process so the bulbs burn out relatively quickly, and the company can accurately calculate the corresponding lifetime under regular usage. They took a random sample of 555 of these new bulbs and calculated their lifetimes. Here are the data and summary statistics:

1.34+2.132 FRACTION (D)

What is the critical value t* , start superscript, times, end superscript for constructing a 90% percent confidence interval for a mean from a sample size of n=18, equals, 18 observations?

1.740

Emilio took a random sample of n=12n=12n, equals, 12 giant Pacific octopi and tracked them to calculate their mean lifespan.

1.796

A marine biologist wanted to construct a ttt interval to estimate the mean weight of marine otters using 98%98%98, percentconfidence. They took a random sample of n=8n=8n, equals, 8 marine otters to measure their weights. These weights were roughly symmetric with a mean of xˉ=4.5 kgxˉ=4.5kgx, with, \bar, on top, equals, 4, point, 5, start text, k, g, end text and a standard deviation of sx=1.1 kgsx​=1.1kgs, start subscript, x, end subscript, equals, 1, point, 1, start text, k, g, end text.

2.998

A fast-food restaurant has an automated beverage machine that dispenses a set amount of liquid based on a size setting.

20 drinks

What is the critical value t∗t∗t, start superscript, times, end superscript for constructing a 99%99%99, percent confidence interval for a mean with 111111 degrees of freedom?

3.106

What is the critical value t∗t∗t, start superscript, times, end superscript for constructing a 99%99%99, percent confidence interval for a mean from a sample size of n=10n=10n, equals, 10 observations?

3.250

Juana is interested in estimating how long it takes students at her school to complete a maze she designed.

39±3.182(4​8.83​)

A doctor took a random sample of n=6n=6n, equals, 6 patients to see how long they each spent in the waiting room. She wants to construct a ttt interval for the mean waiting time with 99%99%99, percent confidence. The times in the sample were roughly symmetric with a mean of xˉ=8.5xˉ=8.5x, with, \bar, on top, equals, 8, point, 5 minutes and a standard deviation of sx=2.8sx​=2.8s, start subscript, x, end subscript, equals, 2, point, 8 minutes.

4.032

Fiona grows large pumpkins and wants to estimate the mean weight of the approximately 500500500 pumpkins in her harvest.

44±3.169(11​6.7​)

Nadia wants to estimate the mean driving range for her company's new electric vehicle.

7 vehicles

What is the critical value t∗t∗t, start superscript, times, end superscript for constructing a 98%98%98, percent confidence interval for a mean from a sample size of n=15n=15n, equals, 15 observations?

2.624

What is the critical value t∗ start superscript, times, end superscript for constructing a 98%, percent confidence interval for a mean with 13 degrees of freedom?

2.650

Tristan made a one-sample zzz interval for a proportion and used the critical value z∗=2.054z∗=2.054z, start superscript, times, end superscript, equals, 2, point, 054.

96