Punith Craźzz
2022-07-11

You can still ask an expert for help

asked 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:

$z=\frac{(mean-sample\text{}mean)}{std\text{}error}$

3. here, I am not sure how to calculate $std\text{}error$. I am considering two formulas:

- $std\text{}erro{r}_{1}=expected\text{}std\text{}dev=\sqrt{0.8\times 0.2}=\sqrt{1.6}=1.264$

- $std\text{}erro{r}_{2}=actual\text{}std\text{}dev=\sqrt{\frac{p\times (1-p)}{sample\text{}size}}=\sqrt{\frac{0.5\times (1-0.5)}{10}}=\sqrt{2.5}=1.58$

4. check the z-value to be less than $-1.65$, if so, reject ${H}_{0}$

Is it makes sense?

- ${H}_{0}$: 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:

$z=\frac{(mean-sample\text{}mean)}{std\text{}error}$

3. here, I am not sure how to calculate $std\text{}error$. I am considering two formulas:

- $std\text{}erro{r}_{1}=expected\text{}std\text{}dev=\sqrt{0.8\times 0.2}=\sqrt{1.6}=1.264$

- $std\text{}erro{r}_{2}=actual\text{}std\text{}dev=\sqrt{\frac{p\times (1-p)}{sample\text{}size}}=\sqrt{\frac{0.5\times (1-0.5)}{10}}=\sqrt{2.5}=1.58$

4. check the z-value to be less than $-1.65$, if so, reject ${H}_{0}$

Is it makes sense?

asked 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.

asked 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?

And we are comparing P to significance level, does it mean P is the probability of making type I error based on the sample?

asked 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.

asked 2022-05-07

For ${H}_{0}:\pi =0.20$, 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 $\hat{\pi}=0$ (in the previous description), but the part where the P-value is $0.012$ is not understood.

It is understood that the score test statistic is $-2.5$ using $n=25$ and $\hat{\pi}=0$ (in the previous description), but the part where the P-value is $0.012$ is not understood.

asked 2022-05-09

Let $\mathcal{X}$ be a sample space, $T$ a test statistic and $G$ be a finite group of transformations (with M elements) from $\mathcal{X}$ onto itself. Under the null-hypothesis the distribution of the random variable $X$ is invariant under the transformations in $G$. Let

$\hat{p}=\frac{1}{M}\sum _{g\in G}{I}_{\{T(gX)\ge T(X)\}}.$

Show that $P(\hat{p}\le u)\le u$ for $0\le u\le 1$ under the null hypothesis

$\hat{p}=\frac{1}{M}\sum _{g\in G}{I}_{\{T(gX)\ge T(X)\}}.$

Show that $P(\hat{p}\le u)\le u$ for $0\le u\le 1$ under the null hypothesis

asked 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 $X=27$.