Practice Math Statistics Problems and Master the Concepts

A survey of students living in a high-rise residence is to be conducted. The residence has 10 floors, 20 rooms per floor, and 2 people per room. What type of sampling method is used if 2 floors are randomly selected and every student on each of those floors is surveyed?

Kelton Bailey 2022-09-28

The denominator of the t score formula for the independent-samples t-test is ______.

1 - population standard error
2 - estimated pooled standard deviation
3 - estimated pooled variance
4 - estimated standard error

Kassandra Mccall 2022-09-27

A public safety association suspects that long distance truck drivers are getting behind the wheel with too little sleep. A sample of 50 drivers yields a sample average of 6 hours of sleep every night with a sample standard deviation 2 hours. Which of the following statements is true ?
a. The sample standard deviation, 2 hours, is a point estimate of the population standard deviation
b. The sample mean, 6 hours, is a point estimate of the population standard deviation.
c. The sample standard deviation, 2 hours, is a point estimate of the population mean
d. The sample mean, 6 hours, is a point estimate of the population mean

Deanna Gregory 2022-09-27

Find the pooled estimate of the standard deviation if n1 = 18, n2 = 14, S1= 3.3, and S2= 2.5.
(Write two decimal places)

amhailim 2022-09-27

When should blood samples for trough drug levels be collected?

Landen Salinas 2022-09-27

Find confidence levels from given intervals
A set of 40 data items, produces a confidence interval for the population mean of $94.93 < μ < 105.07$ . If $\sum x^{2} = 424375$ , find the confidence level.
So the idea of confidence intervals is still rather new to me and one that isn't fully clear in my mind, would someone be able to give me some hints about solving this and explain what they are doing to solve it.
I get that the confidence interval is given by
$\bar{x} - z \frac{σ}{\sqrt{n}} < μ < \bar{x} + z \frac{σ}{\sqrt{n}}$
and that $z = Φ^{- 1} (c)$ where c is the confidence level, however this is as far as my knowledge goes.

Kaila Branch 2022-09-27

What is the mode of the following numbers? $12, 11, 14, 10, 8, 13, 11, 9$
$a 11 b . 10 c . 14 d . 8$

Kolby Castillo 2022-09-26

Let C be a chain complex over a commutative ring R. Let M be a subchain of C such that M is chain equivalent to the zero chain complex. Must C/M and C be chain equivalent ?

fion74185296322 2022-09-26

In what way are voluntary response samples often biased?

babuliaam 2022-09-26

How to show that these groups are isomorphic?
Show that group of all real matrices of form
$[\begin{matrix} x & y \\ - y & x \end{matrix}], (x, y) \neq (0, 0)$
is isomorphic with/to C∖{0} under complex multiplication?
I know two ways to show isomorphism: 1) finding a homomorphic function 2) writing the multiplication table and comparing.

misyjny76 2022-09-26

Fundamental group of GL(n,C) is isomorphic to Z. How to learn to prove facts like this?
I know, fundamental group of GL(n,C) is isomorphic to Z. Actually, I've succeed in proving this, but my proof is two pages long and very technical. I want
1. to find some better proofs of this fact (in order to compare to mine);
2. to find some book or article, using which I can learn, how to calculate fundamental groups and, more generally, connectedness components of maps from one space to another;
3. to find something for the reference, which I can use in order to learn, how to write this proofs nicely, using standard terminology.

misyjny76 2022-09-26

How do you find the exact value of $\cos 2 x$ given $\cos x = - \frac{2}{13}, \frac{π}{2} < x < π$ ?

imchasou 2022-09-26

What is the statistics processes stages and how do we select a simple random ?

fion74185296322 2022-09-26

How are the variance and the standard deviation of a distribution related? What is measublack by the standard deviation?

unjulpild9b 2022-09-26

Whether to use $Z$ or $T$ test statistic for a sample of $50$ , known sample variance and unknown population variance

Grecia Cordova Ramirez2022-09-25

A simple random sample with n =54 provided a sample mean of 24.0 and a sample standard deviation of 4.1.
a. Develop a 90% confidence interval for the population mean (to 1 decimal).
,
b. Develop a 95% confidence interval for the population mean (to 1 decimal).
,
c. Develop a 99% confidence interval for the population mean (to 1 decimal).
,
d. What happens to the margin of error and the confidence interval as the confidence level is increased?

Grecia Cordova Ramirez2022-09-25

A simple random sample of 60 items resulted in a sample mean of 90. The population standard deviation is 13.
a. Compute the 95% confidence interval for the population mean (to 1 decimal).
( , ) I got 93.2 and 86.7, but I keep getting it wrong
b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).
( , )
c. What is the effect of a larger sample size on the margin of error?

lunja55 2022-09-25

Suppose that random variables X and Y vary in accordance with the joint pdf, $f_{X, Y} (x, y) = c (x + y), 0 < x < y < 1.$ . Find c.

Alexus Deleon 2022-09-25

98% confidence interval
For this question from a large amount of data I have calculated that the mean is 44.22, the sample size is 100 and the standard deviation is 22.0773.
From this I am asked to , make the 98% confidence intervals for the (1) true mean µ of the module mark (2) true variance of the module mark
And for each: (a) Determine what quantity to look at, and which distribution table to use, justifying your choice. (b) Determine the number of degrees of freedom, justifying your answer. (c) Calculate the actual intervals.
So far for 1, I have used the z table to look for 99% as I need 1% to the right of 2.33 and 1% to the left of −2.33, so 98% is between $\pm 2.33$ . Giving me
$\bar{x} \pm 2.33 \frac{σ}{\sqrt{n}}$
Which provides me with a 39.08 to 49.36 confidence interval, is this correct? And how would I determine degrees of freedom and go about answering part 2?

Alexus Deleon 2022-09-25

Intro to probability chapter 4 ex 31
A group of 50 people are comparing their birthdays (as usual, assume their birthdays are independent, are not February 29, etc.). Find the expected number of pairs of people with the same birthday, and the expected number of days in the year on which at least two of these people were born.
Solution: Creating an indicator r.v. for each pair of people, we have that the expected number of pairs of people with the same birthday is (50C2 . 1/365) by linearity. Now create an indicator r.v. for each day of the year, taking the value 1 if at least two of the people were born that day (and 0 otherwise). Then the expected number of days on which at least two people were born is
$365 (1 - (364 / 365)^{50} - 50 \cdot (1 / 365) \cdot (364 / 365)^{49})$
Could someone explain how we got the answer ?

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