Recent questions in P-Value

College StatisticsAnswered question

Ariana Montgomery2022-07-19

in a certain population, body weights are normally distributed with a mean of 152 pounds and a standard deviation of 26 pounds. how many people must be surveyed if we want to estimate the percentage who weigh more than 180 pounds? assume that we want 96% confidence that the error is no more than 4 percentage points

College StatisticsAnswered question

Ariana Montgomery2022-07-19

find the point estimate of the proportion of people who wear hearing aids if in a random sample of 898 people, 46 people had hearing aids

College StatisticsAnswered question

Lorena Beard 2022-07-10

Let $X\sim Binomial(n,p)$

$H+0:p\ge .5$

${H}_{1}:p<.5$

How do we evaluate the p-value?

ie. $P(X\ge x\mid p>=.5)$

I have seen settings where this is just interpreted as $P(X\ge x\mid p=.5)$, but I'm not sure how this is the same thing.

$H+0:p\ge .5$

${H}_{1}:p<.5$

How do we evaluate the p-value?

ie. $P(X\ge x\mid p>=.5)$

I have seen settings where this is just interpreted as $P(X\ge x\mid p=.5)$, but I'm not sure how this is the same thing.

College StatisticsAnswered question

slijmigrd 2022-07-08

In the hypotehses testing, I would like to see an intuition how the operator $min$ and the constant $2$ in the computation of $p$-value of a two side alternative $p=2min(F({T}_{0}),1-F({T}_{0}))$ can be derived and understood for a statistics ${T}_{0}$. Here $F$ is the c.d.f.

College StatisticsOpen question

Raghavendra Maila2022-07-07

Resolve F_1 and F_2 into components along the u and v axes and determine the magnitude of these components

College StatisticsAnswered question

slijmigrd 2022-07-07

The data generating process is

$f(x\mid \theta )=\frac{1}{\theta},\phantom{\rule{1em}{0ex}}0\le x\le \theta $

Let ${H}_{1}:\theta =5$ and ${H}_{2}:\theta \ne 5$. Prior probabilities of $\frac{1}{2}$ are assigned to the two hypotheses, and a sample of size $5$ yields a maximum value of $4$. Find the $p$-value here.

According to the definition of $p$-value,

$p=\mathbb{P}(LR\le L{R}^{\ast}\mid {H}_{1}),$

and $L{R}^{\ast}={\left(\frac{4}{5}\right)}^{5}$. I am not sure what to do next. Furthermore, intuitively, if the maxima is equal to $5$ exactly, shall we get an extremely big $p$ or a small one?

$f(x\mid \theta )=\frac{1}{\theta},\phantom{\rule{1em}{0ex}}0\le x\le \theta $

Let ${H}_{1}:\theta =5$ and ${H}_{2}:\theta \ne 5$. Prior probabilities of $\frac{1}{2}$ are assigned to the two hypotheses, and a sample of size $5$ yields a maximum value of $4$. Find the $p$-value here.

According to the definition of $p$-value,

$p=\mathbb{P}(LR\le L{R}^{\ast}\mid {H}_{1}),$

and $L{R}^{\ast}={\left(\frac{4}{5}\right)}^{5}$. I am not sure what to do next. Furthermore, intuitively, if the maxima is equal to $5$ exactly, shall we get an extremely big $p$ or a small one?

College StatisticsAnswered question

Wade Bullock 2022-07-07

I am trying to create an algorithm that could calculate the p-value given the chi-square statistic and the degrees of freedom. Can anyone please point me in the right direction on how I could go about to evaluate the formula and what prerequisites I need to learn before I could do it.

College StatisticsAnswered question

rmd1228887e 2022-07-06

A representative of a potential supplier claims that at least 90% of the equipment manufactured and sold by the company has no defects. You have obtained a sample of equipment usage records from a firm that uses these machines. Of 121 machines in the records, 105 machines have no recorded defects. What is the probability of this event if the supplier’s claim is correct (i.e. The p -value). On the basis of this data, do you believe the representative’s claim?

My thoughts:

The significance level of the test: α = 0.1 (10%)

The percentage of 121 machines that have no recorded defects is 86.7%.

I am not sure how to arrive at the p-value from this data.

My thoughts:

The significance level of the test: α = 0.1 (10%)

The percentage of 121 machines that have no recorded defects is 86.7%.

I am not sure how to arrive at the p-value from this data.

College StatisticsAnswered question

Carly Cannon 2022-07-04

How do I calculate the $p$ value of the following?

Students' height is approximately normal with s.d = $4$ inches, sample = $10$,mean height = $68$ inches.

Calculate the $p$ value corresponding to the following null hypotheses.

${H}_{0}$ = Avg. height is $70$ inches

${H}_{1}$ = Avg. height is not $70$ inches

Students' height is approximately normal with s.d = $4$ inches, sample = $10$,mean height = $68$ inches.

Calculate the $p$ value corresponding to the following null hypotheses.

${H}_{0}$ = Avg. height is $70$ inches

${H}_{1}$ = Avg. height is not $70$ inches

College StatisticsAnswered question

Sam Hardin 2022-07-01

A poll from a previous year showed that $10\mathrm{\%}$ of smartphone owners relied on their data plan as their primary form of internet access. Researchers were curious if that had changed, so they tested ${H}_{0}:p=10\mathrm{\%}$ versus ${H}_{a}:p\ne 10\mathrm{\%}$ where p is the proportion of smartphone owners who rely on their data plan as their primary form of internet access. They surveyed a random sample of $500$ smartphone owners and found that $13\mathrm{\%}$ of them relied on their data plan.

The test statistic for these results was $z\approx 2.236$, and the corresponding $P$-value was approximately $0.025$.

Assuming the conditions for inference were met, which of these is an appropriate conclusion?

a) At the $\alpha =0.01$ significance level, they should conclude that the proportion has changed from $10\mathrm{\%}$.

b) At the $\alpha =0.01$ significance level, they should conclude that the proportion is still $10\mathrm{\%}$.

c) At the $\alpha =0.05$ significance level, they should conclude that the proportion has changed from $10\mathrm{\%}$.

d) At the $\alpha =0.05$ significance level, they should conclude that the proportion is still $10\mathrm{\%}$.

The correct answer is $c$ but why could it not have been $b$? Why is it $c$?

The test statistic for these results was $z\approx 2.236$, and the corresponding $P$-value was approximately $0.025$.

Assuming the conditions for inference were met, which of these is an appropriate conclusion?

a) At the $\alpha =0.01$ significance level, they should conclude that the proportion has changed from $10\mathrm{\%}$.

b) At the $\alpha =0.01$ significance level, they should conclude that the proportion is still $10\mathrm{\%}$.

c) At the $\alpha =0.05$ significance level, they should conclude that the proportion has changed from $10\mathrm{\%}$.

d) At the $\alpha =0.05$ significance level, they should conclude that the proportion is still $10\mathrm{\%}$.

The correct answer is $c$ but why could it not have been $b$? Why is it $c$?

College StatisticsAnswered question

Manteo2h 2022-06-26

Intend to calculate the first and third quartiles of a lognormal distribution with mu and sigma (two lognormal parameters) equal to -0.33217492 and 0.6065058. The expected value and the standard deviation gave me 0.8622153003153145 and 0.6191622375133721.

I intend to calculate the first and third quartiles and found this formula:

${F}^{-1}(p)=exp{\textstyle (}\mu +\sigma {\mathrm{\Phi}}^{-1}(p){\textstyle )}\text{with}0p1$

to calculate the quartiles but I didn't quite understand how to apply it and how to calculate the p-value. How can I find out the first and third quartiles of this distribution?

I intend to calculate the first and third quartiles and found this formula:

${F}^{-1}(p)=exp{\textstyle (}\mu +\sigma {\mathrm{\Phi}}^{-1}(p){\textstyle )}\text{with}0p1$

to calculate the quartiles but I didn't quite understand how to apply it and how to calculate the p-value. How can I find out the first and third quartiles of this distribution?

College StatisticsAnswered question

migongoniwt 2022-06-25

Calculation of $p$-value: Fabric water properties, ${H}_{0}:\mu \le 55\mathrm{\%}$ versus ${H}_{A}:\mu >55\mathrm{\%}$;

$n=15,\overline{x}=59.81\mathrm{\%},s=4.94\mathrm{\%}$

I understand that the hypothesized mean is $55$ samples mean is $59.81$ sample standard deviation is $4.94$ sample size is $15$. And I use the $t$-test, I have gotten $3.77106$. In this circumstance, how can I get the $p$-value, and what is different between critical value and $p$-value?

$n=15,\overline{x}=59.81\mathrm{\%},s=4.94\mathrm{\%}$

I understand that the hypothesized mean is $55$ samples mean is $59.81$ sample standard deviation is $4.94$ sample size is $15$. And I use the $t$-test, I have gotten $3.77106$. In this circumstance, how can I get the $p$-value, and what is different between critical value and $p$-value?

College StatisticsAnswered question

Dania Mueller 2022-06-24

The summary of that regression shows that one of my variable has a big p-value (0.705). Should I include that variable when writing the the y hat equation?

College StatisticsAnswered question

abbracciopj 2022-06-24

Suppose that for every α∈(0,1) we have a size α test with rejection region Rα. Then,

$\text{p-value}=inf\{\alpha :T({X}^{n})\in {R}_{\alpha}\}$

That is, the p-value is the smallest level at which we can reject ${H}_{0}$.

what is this exponent $n$. What does ${X}^{n}$ mean?

$\text{p-value}=inf\{\alpha :T({X}^{n})\in {R}_{\alpha}\}$

That is, the p-value is the smallest level at which we can reject ${H}_{0}$.

what is this exponent $n$. What does ${X}^{n}$ mean?

College StatisticsAnswered question

gledanju0 2022-06-24

${X}_{i}\sim Bern(p)$, $Y=\sum _{i=1}^{N}{X}_{i}$ and ${H}_{0}:p\ge 0.5$ vs ${H}_{1}:p<0.5$ with $\alpha =0.05$.

I have to find the $p$-value at $n=30$ and $y=5$.

I'm not sure if this correct, but I figured the $p$-value was simply:

$P(Y\le 5)=\sum _{i=1}^{5}{\textstyle (}\genfrac{}{}{0ex}{}{30}{y}{\textstyle )}(0.5{)}^{y}(0.5{)}^{30-y}$

which works out to be $0.00016$.

If this is correct, then why have I been given $\alpha $?

I have to find the $p$-value at $n=30$ and $y=5$.

I'm not sure if this correct, but I figured the $p$-value was simply:

$P(Y\le 5)=\sum _{i=1}^{5}{\textstyle (}\genfrac{}{}{0ex}{}{30}{y}{\textstyle )}(0.5{)}^{y}(0.5{)}^{30-y}$

which works out to be $0.00016$.

If this is correct, then why have I been given $\alpha $?

College StatisticsAnswered question

kokoszzm 2022-06-22

Suppose a coin with probability $p$ of heads is repeatedly flipped until $10$ heads appear. Call this number $X$. Find the p-value of ${H}_{0}:p=0.5$ versus the alternate ${H}_{a}:p\ne 0.5$ using the test statistic $|X-20|$ if $X=27$.

College StatisticsAnswered question

Ezekiel Yoder 2022-06-20

A data between rating of the restaurant and the approximate price of food in the restaurant. After doing Hypothesis testing. The pearson correlation coefficient was found to be 0.33 whereas p value was calculated much lesser than .05. Which means we have to accept our Alternate hypothesis as the finding is statistically significant. Our Alternate Hypothesis was that there is some relation between the two variables. Which is contrary to what we got as the coefficient i.e 0.33 which says there is no relation between the two.

College StatisticsAnswered question

Kassandra Ross 2022-06-20

From a collection of objects numbered $\{1,2,....,K\}$ objects are picked and replaced. We want to test ${H}_{0}:K=100000$ against ${H}_{1}<100000$, with the highest ranking number $M$ of our sample as test statistic. We find for our realisation for $M$ the value $81115$.

What is the $P$ value?

The correct answer is: $0.015$

I know that the definition of the $p$-value is:

The p-value is the probability of getting the observed value of the test static or a value with even greater evidence against ${H}_{0}$, if the hypothesis is actually true

or in formula form $P(T\ge t)$

I have the following questions:

What are $T$ and $t$?

I think that distribution is uniform, but how do I calculate the $p$-value?

What is the $P$ value?

The correct answer is: $0.015$

I know that the definition of the $p$-value is:

The p-value is the probability of getting the observed value of the test static or a value with even greater evidence against ${H}_{0}$, if the hypothesis is actually true

or in formula form $P(T\ge t)$

I have the following questions:

What are $T$ and $t$?

I think that distribution is uniform, but how do I calculate the $p$-value?

College StatisticsAnswered question

Oakey1w 2022-06-15

${H}_{0}\beta =0,{H}_{a}\beta \ne 0$.

The test itself is a generalized likelihood ratio. The test statistic is the ratio LR:

$LR=\frac{L(\beta =0)}{argma{x}_{\beta \in R}L(\beta )}$

Where $L$ is the likelihood function.Then $-2ln(LR)$ follows a ${\chi}_{1}^{2}$.

I am trying to calculate the p-value for a specific value of LR. Say I look for at a ${\chi}_{1}^{2}$ table (or online calc) and find out that

$P({\chi}_{1}^{2}\ge -2ln(LR))=\alpha $

Is $\alpha $ my final $p$-value?

Or do I need to account for the fact that the test is two-sided and set the $p$-value $=2\ast \alpha $?

The test itself is a generalized likelihood ratio. The test statistic is the ratio LR:

$LR=\frac{L(\beta =0)}{argma{x}_{\beta \in R}L(\beta )}$

Where $L$ is the likelihood function.Then $-2ln(LR)$ follows a ${\chi}_{1}^{2}$.

I am trying to calculate the p-value for a specific value of LR. Say I look for at a ${\chi}_{1}^{2}$ table (or online calc) and find out that

$P({\chi}_{1}^{2}\ge -2ln(LR))=\alpha $

Is $\alpha $ my final $p$-value?

Or do I need to account for the fact that the test is two-sided and set the $p$-value $=2\ast \alpha $?

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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.