Practice Math Statistics Problems and Master the Concepts

Heights for men are distributed according to a Normal model, with an average of 69 inches and a standard deviation of 3
inches. The tallest 30% of men will be at what height or taller? Round your answer to the nearest hundredth (two decimal
places), if necessary.

Dominick Blanchard 2022-05-10

If an atom is put into motion will a constituent electron's wave spread over a LARGER region of space and will its energy be more dissipated?
My understanding is that a quantum event such as an electron moving between atomic levels takes place smoothly and continuously over a small discrete time interval during which time its energy will be relatively unstable.
Also an electron can spread out into a wave that extends over a region of space.
If an atom is put into motion will the electron's wave spread over a LARGER region of space than when stationary resulting in less energy per unit volume of space?

Brooklynn Hubbard 2022-05-10

in order to remember stuff i need to understand their reason. Right now i cannot remember what is type 1 error and what is type 2 error why is the reason type 1 is false positive?

Karissa Sosa 2022-05-10

"A certain disease has an incidence rate of 2%. If the false negative rate is 10% and the false positive rate is 1%, compute the probability that a person who tests positive actually has the disease."
Why do we need to use Bayes' Theorem for this question?

An MP3 manufacturer claimsthat 65% of teenagers 13 to 16 years old have their own MP3 players.
A researcher wishes to test the claim and selects a random sample of 80 teenagers. She finds that
57 have their own MP3 players. At � = 0.05, should the claim be rejected?

The average credit card debt for a recent year was $9205. Five years earlier the average credit card
debt was $6618. Assume sample sizes of 35 were used and the population standard deviations of
both samples were $1928. Find the 95% confidence interval of the difference in means.

deformere692qr 2022-05-09

We want to make an hypothesis test for the mean value $μ$ of a normal population with known variance $σ^{2} = 13456$ , using a sample of size $n = 100$ that has sample mean value equal to $562$ .
Calculate the $p$ -value.
Make the test with significance level $1 %$ about if the population mean value from which the sample comes from is greater than $530$ using the $p$ -value.
For the first one, about the $p$ -value, do we have to calculate $P (\frac{530 - 562}{\frac{σ}{\sqrt{n}}})$ ?
And for the second we have to check the $p$ -value with the significance level, right?

Adelyn Rodriguez 2022-05-09

Descartes rule of sign can be used to isolate the intervals containing the real roots of a real polynomial. The rule bounds the number of roots from above, that is, it is exact only for intervals having zero or one root. In methods like VCA, VAS and similar, it is used to count the number of sign changes to determine the number of roots.
My question is, what to do if the rule reports, say, two sign changes for interval which does not contain any roots?

motorinum6fh9v 2022-05-09

What is the mode of the numbers: 153, 157, 163, 165, 166, 169, 170, 173, 176, 185?

Jace Wright 2022-05-09

Consider testing $H_{0} : θ \geq 3 vs H_{a} : θ < 3$ using a test in which the null hypothesis is rejected when the statistic $T = min {X_{1}, . . ., X_{n}}$ , for example of size $n$ has small values. Compute the $p$ -value using the sample $3.11, 3.3, 3.46$

Alexis Meyer 2022-05-09

What is the range in the set of data below 35, 39, 25, 57 62, 46, 53, 41?

Eve Dunn 2022-05-09

A(n) __________ summarizes how risk management will be perfomed on a particular project.
$\circ$ Risk response plan
$\circ$ Quantitative risk analysis
$\circ$ Risk management plan
$\circ$ Qualitative risk analysis

Osmarq5ltp 2022-05-09

Samples are taken from two different types of honey and the viscosity is measured.

Honey A:
Mean: 114.44
S.D : 0.62
Sample Size: 4

Honey B:
Mean: 114.93
S.D: 0.94
Sample Size: 6

Assuming normal distribution, test at 5% significance level whether there is a difference in the viscosity of the two types of honey?

Here's what I did:

I took my null hypothesis as $μ$ B - $μ$ A = 0 and alternative hypothesis as $μ$ B - $μ$ A $\neq$ 0

Then I did my calculations which were as following:

Test Statistic = (B -A ) - ( $μ$ B - $μ$ A) / sqrt {(variance B / sample size B) + (variance A / sample size A)}

This gave me test statistic as = 0.49/0.49332 that is equal to 0.993

However the test statistic in the book solution is given as 0.91. What am I doing wrong?

velinariojepvg 2022-05-09

True or false: if $a_{n}$ is any decreasing sequence of positive real numbers and $b_{n}$ is any sequence of real numbers converges to $0$ , then $\frac{a_{n}}{b_{n}}$ diverges.

tuehanhyd8ml 2022-05-09

how are the two definitions related?
function definitions
$u (x)$ : this functions takes in a vector $x \in R^{n}$ and spits out a value $u (x) \in R$
$r (x) = \frac{- u^{″} (x)}{u^{'} (x)}$ (risk coefficient)
$k (x) = \frac{| u^{'} (x) |}{(1 + (u^{'} (x))^{2})^{3 / 2}}$
In class, we've been using utility functions that have a constant absolute risk version coefficient. This function is:
$u (x) = (\frac{4}{3}) (1 - (1 / 2)^{x / 50})$
Thus, $u^{'} (x) = \frac{- (2 * (1 / 2)^{x / 50} \ln (1 / 2))}{75}$
$u^{″} (x) = \frac{- ((1 / 2)^{x / 50} l o g (1 / 2)^{2}}{1875}$
And we have:
$r (x) = \frac{- \ln (1 / 2)}{50}$
However, curvature is:
$k (x) = \frac{1}{((4 (\frac{1}{2})^{x / 25} \frac{l o g (1 / 2)^{2}}{5625} + 1)^{3 / 2}} = \frac{1}{(.00034166 (\frac{1}{2})^{x / 50} + 1)^{3 / 2}}$
So, clearly this line does not have constant curvature by the geometric definition. This is also obvious when looking at a graph of $u (x)$ . So, I'm struggling to relate the two measures. Is Arrow-Pratt discussing the relationship between slope and curvature?

sembuang711q6 2022-05-09

There are 3 lottery tickets one can choose from:
$\begin{array}{rr} A l t e r n a t i v e s & C h a n c e s & O u t c o m e \\ A & 1 / 1000 & $ 1000 \\ 999 / 1000 & $ 0 \\ B & 1 / 100 & $ 100 \\ 99 / 100 & $ 0 \\ C & 1 / 2000 & $ 1000 \\ 1 / 200 & $ 100 \\ 1989 / 2000 & $ 0 \end{array}$
And the formula for computing the probabilities of final outcomes when a coin is flipped between lotteries $A & B$ yields
$P_{$ 1000} = \frac{1}{2} \frac{2}{2000} = \frac{1}{2000}$
$P_{$ 100} = \frac{1}{2} \frac{20}{1000} = \frac{10}{1000}$
$P_{00} = 1 - P_{$ 1000} - P_{$ 100}$
$= \frac{1989}{2000}$
So there are 3 different probabilities here. The first one, $P_{$ 1000}$ is the probability of the outcome being $1000$ dollars, which is (the probability of getting lottery A from the coin flip) x (the probability of the outcome being $1000$ dollars). That makes sense from the table above. But the second one, $P_{$ 100}$ , the probability of the outcome being $100$ dollars should be $\frac{20}{2000}$ or $\frac{1}{100}$ . Why then is it $\frac{20}{1000}$ ???

othereyeshmt4l 2022-05-09

Describe the two basic functions of the qualitative risk analysis process and explain why a project manager should perform a qualitative risk analysis prior to quantitative risk analysis.

kazue72949lard 2022-05-09

Describe the risk analysis approach and the steps in a detailed or formal risk analysis

Flakqfqbq 2022-05-09

Let $X$ be a sample space, $T$ a test statistic and $G$ be a finite group of transformations (with M elements) from $X$ onto itself. Under the null-hypothesis the distribution of the random variable $X$ is invariant under the transformations in $G$ . Let
$\hat{p} = \frac{1}{M} \sum_{g \in G} I_{{T (g X) \geq T (X)}} .$
Show that $P (\hat{p} \leq u) \leq u$ for $0 \leq u \leq 1$ under the null hypothesis

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