Practice Math Statistics Problems and Master the Concepts

How one derives significance test for pearsons correlation coefficient?
I am exploring statistics and probability. What upsets me, only ready to use algorithms are present in the books. But no example how one derives a significance test, where from the test statistics come from etc. At the moment I am interesten in Pearsons coefficient significance test, but really derivation of any popular test will be helpful for me.

Case Nixon 2022-05-22

$X_{1} . . . X_{n}$ ~ Bernoulli(p) independent. I also have the following test hypothesis: $H_{0} : p = p_{0}$ and $H_{1} : p > p_{0}$ . I define my test as follows:
$T :$ I refuse $H_{0}$ in favour of $P_{1}$ if the number of successes is very high.
Now suppose $p_{0} = 0.6$ and $n = 20$ , we find that we have 18 successes.
Find the p-value of the test.
Now this is what I have done:
$p - v a l u e = P (\sum x_{i} \geq 18)$ $= 0.0005240494$ However confronting it with the command:
$b i n o m . t e s t (18, 20, p = .6, a l t e r n a t i v e = g r e a t e r)$
It is not right (by a factor of 10). My problem is that I am not able to correctly asses what the "number of succession is very high". How do I work around this?

realburitv4 2022-05-22

How do you determine the highest level of significance (in decimal form) at which the null hypothesis will not be rejected?
Let's say for instance I got a p-value of $0.001$ and a test statistic of $3.273$ , then is $0.0005$ the highest level of level of significance at which $H_{0}$ will not be rejected?

Aiden Barry 2022-05-22

Maria's phone bills were $95, $67, $43, and $115. What was the mean of her phone bills?

infogus88 2022-05-21

The test statistic is z = 2.75, the critical value is z = 2.326. The probability value is_________.
Select one:
a. not measurable
b. greater than the significant level
c. equal to the significant level
d. less than the significant level

Isaiah Farrell 2022-05-21

What happens to the mean, median and mode for the data 14, 15, 22, 15, 2, 16, 17, and 13 if the outlier is eliminated?

velitshh 2022-05-21

A new cream that advertises 52% of women over the age of 50 will experience skin improvement from using their product. A study was conducted in which a sample of 170 women over the age of 50 used the new cream for 6 months. Of those 170 women, 76 of them reported skin improvement (as judged by a dermatologist). Is this evidence that the cream will improve the skin of less than 52 % of women over the age of 50? Perform a hypothesis test using the 0.05 level of significance.
Set up a null and alternate hypothesis.

Jerry Villegas 2022-05-21

A student has earned the following scores on four 100-point math tests: 66, 70, 85, 88. What score must the student earn on the fifth to earn an average grade of 80 for those five tests?

Hayley Sanders 2022-05-20

For the data set 6, 34, 12, and 14, what is the range?

Scolfaro2y 2022-05-20

Mean vs. Median: When to Use?
I know the difference between the mean and the median.
- The mean of a set of numbers is the sum of all the numbers divided by the cardinality.
- The median of a set of numbers is the middle number, when the set is organized in ascending or descending order (and, when the set has an even cardinality, the mean of the middle two numbers).
It seems to me that they're often used interchangeably, both to give a sense of what's going on in same data.
Do they mean (pun intended) different things? When should one be used over the other?

Belle Park2022-05-20

vestpn 2022-05-19

How do you find the average of one number?

If I have the following Hypothese:
H1: Women tend to watch romantic films more than men
Apparently it's a chi-square because I'm measuring relationships between expected frequency and Observed frequency and also because Gender is on the nominal level. But what if this is designed for a survey in which questions are on the nominal, Ordinal and interval level (Likert scale - differential sementic) will the outcome still be a Chi-square?

Alaina Holt 2022-05-14

What is the mean, median, mode, and range of 7.6, 7.6, 6.1, 6, 14.3?

hisyhauttaq84w 2022-05-14

The value $α$ that represents the probability of type I error is often referred to as the __________________ of the test.
The vertical deviationsy1-y^1,y2-y^2,...,yn-y^nfrom the estimated regression line are referred t as the. $The vertical deviations y_{1} - {\hat{y}}_{1}, y_{2} - {\hat{y}}_{2}, . . ., y_{n} - {\hat{y}}_{n} from the estimated regression line are referred t as the________.$
$When the estimated regression line is obtained via the principle of least squares, the sum of the residuals y; - \hat{y}; (i = 1, 2, 3, . . ., n) should in theory be$

Daphne Haney 2022-05-13

Does gas spread out equally everywhere?
"Gases can fill a container of any size or shape. It doesn't even matter how big the container is. The molecules still spread out to fill the whole space equally. That is one of their physical characteristics."
If a fixed quantity of gas is let out in a limited space, will it spread out equally and maintain a fixed gas distribution throughout the space?
Or, does it go where the gravitational pull is maximum? And what factors affect the distribution of gas in a given area?

Osmarq5ltp 2022-05-13

How do you find the mean, median and mode of 1, 2, 3, 4, 5, 6, 7, 8, 9?

affizupdaftf3opg 2022-05-13

Why does the wavefunction of a particle spread out after a measurement?
Quantum mechanics states that the wave packet of a particle "spreads-out" in position again after a measurement on this particle has been made. Is this spreading or "dispersion" caused by inherent properties of the wavefunction itself (eg according to the Uncertainty Principle), or is it due to the interaction with the environment (or both)? Does the wavefunction of a free, non-interacting particle also show this behaviour?

For the provided sample mean, sample size, and population standard deviation, complete parts (a) through (c) below.
x=32,
n=100,
σ=3
Question content area bottom
Part 1
a. Find a 95% confidence interval for the population mean.

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