P-Value: Comprehensive Solutions and Explanations

A tailor thinks that about $75 %$ of customers are satisfied with service. A random sample of $15$ customers, $8$ said they were satisfied. Calculate whether this is plausible at $5 %$ significance level.
I figured that $μ = 0.6$ , and $\bar{x} = 8 / 15$ , but I'm not sure how to get the variance. Can you assume satisfaction follows a Bernoulli distribution and calculate variance as $(0.75 (1 - 0.75)) / n$ ?

Leland Morrow 2022-06-07

When performing a hypothesis testing z-test we can in the end determine the p-value using a standard normal curve after determine the z-score. Is the standard normal curve derived from my sample, that is using central limit theorem and then standardize the curve?

Baylee Newman 2022-06-04

I have an f-value = $2.3$ and am trying to determine if I should reject the null at the $1 %$ level. Do I need to calculate the p-value to solve this question? What's the best way to get the p-value if I have the f-statistic, degrees of freedom, and the data points?

Trystan Yates 2022-06-04

A drug claims to cure patients in 80% of all cases. A sample of 10 patients was taken, 5 got cured, 5 not. I need to decide if the manufacturer should change their claim. Assume 5% to be the significance level.
- $H_{0}$ : p = 0.8
- $H_{A}$ : p < 0.8
So, my approach:
1. sample size = 10, p = 0.5, std dev = 0.25
2. calculate the z-value for the sample:
$z = \frac{(m e a n - s a m p l e m e a n)}{s t d e r r o r}$
3. here, I am not sure how to calculate $s t d e r r o r$ . I am considering two formulas:
- $s t d e r r o r_{1} = e x p e c t e d s t d d e v = \sqrt{0.8 \times 0.2} = \sqrt{1.6} = 1.264$
- $s t d e r r o r_{2} = a c t u a l s t d d e v = \sqrt{\frac{p \times (1 - p)}{s a m p l e s i z e}} = \sqrt{\frac{0.5 \times (1 - 0.5)}{10}} = \sqrt{2.5} = 1.58$
4. check the z-value to be less than $- 1.65$ , if so, reject $H_{0}$
Is it makes sense?

Shomalit4ob5 2022-06-01

Find the $p$ -value (manually) of the following
Hypothesis testing.
$H_{0} : μ \leq 3 vs H_{1} : μ > 3$
The main thing I know is that
$P (R e j ∣ μ \leq 3) = P (X \geq 3 ∣ μ \leq 3) = e^{- 1} \approx 0.36$
Can I use the $z$ value and use the formula probability of $z$ ?

Isabela Sherman 2022-05-29

Tell me about this $p$ -value in relatively simple but not too simple terms.
I've been reading many academic publications of late and come across it quite a few times without having a clear idea what it means. It's something about probability, isn't it? If it's less than, I believe, $0.05$ , then it's, whatever it is, not a simple coincidence but a real correlation, right?

Isabel Espinoza2022-05-26

Find the critical value z a/2 that Corresponds to the confidence level of 80%

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?

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?

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 $3.11, 3.3, 3.46$

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

Daphne Fry 2022-05-08

Let $X_{i}$ be Gaussian random variables with $μ$ = $10$ and $σ^{2}$ = $1$ . We decide to use the test statistic $\hat{μ}$ = $\frac{1}{20} \sum_{i = 1}^{20} X_{i}$ and following tests:
$| \hat{μ} - 10 | > τ$ : Reject $H_{0}$
$| \hat{μ} - 10 | \leq τ$ : Cannot reject $H_{0}$
1) Find $τ$ if you want to have $95 %$ confidence in the test.
2) You find that $\hat{μ} = 10.588$ . Do you reject $H_{0}$ ? If so, what is the p-value?
Using textbook equations, I found out that for
1) $τ$ = $σ_{\hat{μ}}$ = $1.96 \sqrt{\frac{1}{20}}$ $= 0.392$
2) $| 10.588 - 10 | = 0.588 > 0.392 \to$ Reject $H_{0}$
p-value $= 0.003$

Direkotogbkmn 2022-05-08

p-values behave uniformly. Now as p(np) is fixed and n goes to infinity, binomial converges to normal(Poisson). Now suppose I take random binomial samplings and fir normal(Poisson) to it, for say n = 1000. Will my p-value still be uniformly distributed or as binomial converges to normal(Poisson), p-values mostly will be in 0.8-1?

bedblogi38am 2022-05-07

For $H_{0} : π = 0.20$ , for instance, the score test statistic is $Z (s) = - 2.50$ , which has two-sided P-value $0.012 < 0.05$ , so $0.20$ does not fall in the interval.
It is understood that the score test statistic is $- 2.5$ using $n = 25$ and $\hat{π} = 0$ (in the previous description), but the part where the P-value is $0.012$ is not understood.

Brooklynn Hubbard 2022-05-07

I'm confused about the interpretation of P value in hypothesis testing. I know that we set significance level as 0.05 which is the threshold we set for this test so that it won't suffer from Type I error by 5%.
And we are comparing P to significance level, does it mean P is the probability of making type I error based on the sample?

Justine Webster 2022-04-07

Are there any theoretical considerations between p-value and the Bayesian statistics? I mean say, any theorem regarding both of these two concepts at a time.

Dealing with statistics and probability as a college student, one of the most common tasks that you might face is evaluating the P value significance as you work with equations or seek answers to the most common tasks. The P value stands for the probability value and strives to represent a number regarding how your specific data would work in relation to the null hypothesis when you are performing a statistical test. Even when you have a P value calculator, you may still find our selection of answers quite helpful for your statistical task, be it finances related or engineering.

P-Value Uncovered: Discover the Secrets with Plainmath's Expert Help