Recent questions in Significance tests

Significance tests
Answered

Ernesto Wagner
2022-11-23

My answer: Null = 209500.0 alternative = .01

I'm being told that these my answers are not correct. I have no idea why. Any help would be appreciated!

Significance tests
Answered

Abdiel Mays
2022-11-13

Confusion:

One of my friends gives this answer:

The hypothesis model will be

${H}_{o}:\mu ={\mu}_{o}$

${H}_{A}:\mu \ne {\mu}_{o}$

Type I error $\alpha $ is the probablity of rejecting the null hypothesis ${H}_{o}$

Thus $p=\alpha $

I think it's not correct, because Type I error is the the probablity of rejecting the null hypothesis ${H}_{o}$ when ${H}_{o}$ is true , and α means the size of test is no larger than $\alpha $, so I think there are some differences between these two concepts.

So who is wrong? why? and what the correct answer should be?

Significance tests
Answered

reevelingw97
2022-11-11

(a) how many students will fail to reject the null hypothesis given that the null hypothesis is false

(b) how many students will reject the null hypothesis given that the null hypothesis is true.

I have tried searching online but so far all sites only show how to calculate the probability that at least one type I error will be made. Any assistance will be greatly appreciated.

Significance tests
Answered

Audrey Arnold
2022-11-11

Suppose that as a personnel director, you want to test the perception of fairness of two methods of performance evaluation. 63 of 78 employees rated Method 1 as fair. 49 of 82 rated Method 2 as fair. A 99% confidence interval for ${p}_{1}$−${p}_{2}$ (where ${p}_{1}$ = 63/78 and ${p}_{2}$ = 49/82) is as follows:

${p}_{1}-{p}_{2}\pm 2.58\sqrt{\frac{{p}_{1}(1-{p}_{1})}{{n}_{1}}+\frac{{p}_{2}(1-{p}_{2})}{{n}_{2}}}$

$0.029\u2a7d{p}_{1}-{p}_{2}\u2a7d0.391$

At the 0.01 level of significance the Z score is

$Z=\sqrt{\frac{p(1-p)}{{n}_{1}}+\frac{p(1-p)}{{n}_{2}}}$

(where p = $({x}_{1}+{x}_{2})/({n}_{1}+{n}_{2})=0.70$ but sometimes a different formula $p=({p}_{1}+{p}_{2})/2$ is also used)

Z = 2.90

Both tests indicate that there is evidence of a difference.

But you could also find the Z score using the standard deviation formula in the first method to be 2.993. Why are the Z scores different? Where do the formulas for finding the standard deviation come from?

Significance tests
Answered

Adison Rogers
2022-11-06

Confusion:

One of my friends gives this answer:

The hypothesis model will be

${H}_{o}:\mu ={\mu}_{o}$

${H}_{A}:\mu \ne {\mu}_{o}$

Type I error $\alpha $ is the probablity of rejecting the null hypothesis ${H}_{o}$

Thus $p=\alpha $

I think it's not correct, because Type I error is the the probablity of rejecting the null hypothesis ${H}_{o}$ when ${H}_{o}$ is true , and α means the size of test is no larger than $\alpha $, so I think there are some differences between these two concepts.

So who is wrong? why? and what the correct answer should be?

Significance tests
Answered

Jacoby Erickson
2022-10-25

You throw the coin until you obtain heads for the first time.

You want to test ${H}_{0}:p=1/2$ against ${H}_{1}:p<1/2$. You reject ${H}_{0}$ in favor of ${H}_{1}$ if $T\ge k$, where T is the number of the throw which yielded heads for the first time and k an integer.

Determine the smallest value of k corresponding to the level of significance α=0.01.

Answer k=8

I can't find the correct solution for this question, how it's possible to have ${H}_{1}:p<1/2$ and then they say that we reject ${H}_{0}$ in favor of ${H}_{1}$ if $T\ge k$, shouldn't they be in the same direction?

I have to compute $P(T>k|{H}_{0})=P(T>k|p=1/2)$ right? How can I compute it?

Significance tests
Answered

Emilio Calhoun
2022-10-24

The test statistic is 13.277 under the tested null hypothesis. write a recommended null hypothesis and an alternative hypothesis. Briefly describe your conclusion on this test at the 0.01 significance level.

Significance tests
Answered

erwachsenc6
2022-10-23

A sample of 25 answers has an average=forty five and a variance=25.

Significance tests
Answered

Lilah Hurst
2022-10-21

Significance tests
Answered

Winston Todd
2022-10-18

$${f}_{p,\lambda}(x)=\frac{{\lambda}^{p}}{\mathrm{\Gamma}(p)}\cdot {x}^{p-1}\cdot {e}^{-\lambda x}$$

with p=10 and ${H}_{0}:\lambda =2$ or ${H}_{1}:\lambda =4$ and $\alpha =0.001$

I want to apply the Lemma of Neyman Pearson which states:

Be c>0 fixed and chosen in the way that $A(c)=\{x\in B:\frac{{f}_{0}(x)}{{f}_{1}(x)}\ge c\}$ such that ${\mathbb{P}}_{{H}_{0}}(X\in A(c))=\alpha $

Then the test with the region A(c) among all tests with significance level $\alpha $ is the most powerful.

I am now trying to calculate A(c), but got stuck. I have:

$${\int}_{A(c)}{f}_{0}(x)dx={\int}_{A(c)}\frac{{\lambda}^{p}}{\mathrm{\Gamma}(p)}\cdot {x}^{p-1}\cdot {e}^{-\lambda x}dx=\alpha .$$

But I don't know how to get A(c) from this integral...

$\frac{{f}_{0}(x)}{{f}_{1}(x)}=\frac{1}{1024}\cdot {e}^{2x}$

Significance tests
Answered

Kasey Reese
2022-10-17

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?

Significance tests
Answered

Tara Mayer
2022-10-16

whenever i am seeking to get into data (once more), i am constantly lost at speculation trying out.

My simple question is - why can we form a null hypothesis as a negation of what we need to show within the first region, and most effective then can we show or disprove the null speculation?

Why do we do it at all, in preference to just proving the authentic speculation?

Significance tests
Answered

Kevin Charles
2022-10-11

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%.

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

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

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

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

Significance tests
Answered

dalllc
2022-10-09

I have solved this question but I don't know whether the answer is correct or not.

Solution:

${H}_{0}$: mean = 120 (null hypothesis) ${H}_{1}$: mean > 100 (alternative hypothesis)

we will use z test as the sample count is more than 30

$z=\frac{120-100}{60\sqrt{64}z}=2.67$

at 5% of significance, the critical value of z is 1.96. Since the z value we obtained is more than 1.96, so we reject the null hypothesis and therefore the mean price of the test is more than 100

Significance tests
Answered

Jamarcus Lindsey
2022-10-08

I have solved this question but I don't know whether the answer is correct or not.

Solution:

${H}_{0}$: mean = 120 (null hypothesis) ${H}_{1}$: mean > 100 (alternative hypothesis)

we will use z test as the sample count is more than 30

$z=\frac{120-100}{60}\sqrt{64}z=2.67$

at 5% of significance, the critical value of z is 1.96. Since the z value we obtained is more than 1.96, so we reject the null hypothesis and therefore the mean price of the test is more than 100

Significance tests
Answered

kasibug1v
2022-09-09

Consider a population of independent light bulbs with an exponential lifetime distribution with mean $\mu $. It is claimed that their expected lifetime is 1000 hours. A definition of a 100(1−$\alpha $)% confidence interval obtained from an observation to is the set of all ${\mu}_{0}$ which are not rejected in a test of a null hypothesis ${\mu}_{0}$ against an alternative hypothesis $\ne $.

One particular light bulb fails after 622 hours. Solve the equations of the two significance probabilities Pr(T "$$" 622 |${\mu}_{0}$) = 0.05 (for a test of ${\mu}_{0}$ versus ${\mu}_{0}$) and Pr(T "$$" 622 |${\mu}_{0}$ = 0.05 (for a test of ${\mu}_{0}$ versus ${\mu}_{0}$) for $\mu $. Determine the range of values of $\mu $ such that both of the probabilities Pr(T "$$" 622 | $\mu $) and Pr(T "$$" 622 |$\mu $) are at least 0.05. (This range gives an equi-tailed 90% confidence interval for $\mu $.)

I don't seem to understand what they mean by 'solve the equations'. Do I have to find a specific value for T or compute Pr(T $\ge $ 622 |${\mu}_{0}$), Pr(T $\le $ 622 |${\mu}_{0}$) and compare with 0.05? I believe I will get the second part after I understand this bit.

Significance tests
Answered

gsragator9
2022-09-01

test the hypothesis the variance for economists equal the variance for the historians. Use a .05 significance level, a two tail test and the following data :

economist historian

var 120 90

n 46 38

ntsibengshete81
2022-08-25

A local newspaper claims that 90% of its online readers are under the age

Significance tests
Answered

gorgeousgen9487
2022-07-14

You have a fair coin that you keep on flipping. After every flip, you perform a hypothesis test based on all coin flips thus far, with significance level $\alpha $, where your null hypothesis is that the coin is fair and your alternative hypothesis is that the coin is not fair. In terms of $\alpha $, what is the expected number of flips before the first time that you reject the null hypothesis?

Edit based on comment below: For what values of α is the answer to the question above finite? For those values for which it is infinite, what is the probability that the null hypothesis will ever be rejected, in terms of $\alpha $?

Edit 2: My post was edited to say "You believe that you have a fair coin." The coin is in fact fair, and you know that. You do the hypothesis tests anyway. Otherwise the problem is unapproachable because you don't know the probability that any particular toss will come up a certain way.

Significance tests
Answered

Wisniewool
2022-07-14

A researcher believes that the stock market performance and the property market performance in Singapore are associated. Describe one (1) statistical approach the researcher would implement to determine the association between the performances of these two markets. Explain their association and the factors that affect their association.

Almost all significance test practice problems that you will encounter below help to find solutions to your questions as the answers deal with the same equations that have been used. Start with any significance test example and you will understand that you only have to change variables to determine each value. It's exactly what makes significance test equation so popular as it provides help with more advanced probability concepts. As you look through significance test questions, look for similar patterns as these are where you must start regardless of whether you deal with a complex engineering project or statistical analysis.