Mathematics, 28.11.2019 06:31 shadow56

For the hypothesis test h0: μ = 10 against h1: μ > 10 and variance known, calculate the pvalue for each of the following test statistics.(a) z0 = 2.05 (b) z0 = −1.84 (c) z0 = 0.4

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Answer from: my7butterflies

a) p_v =P(Z2.05)=1-P(z

b) p_v =P(Z-1.84)=1-P(z

c) p_v =P(Z0.4)=1-P(z

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis: $\mu=10$

Alternative hypothesis: $\mu 10$

If the random variable is distributed like this: $X \sim N(\mu,\sigma)$

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

$z_o=\frac{\bar X -\mu}{\sigma}$

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

p_v =P(Z2.05)=1-P(z

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

p_v =P(Z-1.84)=1-P(z

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

p_v =P(Z0.4)=1-P(z

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say $\alpha=0.05$ . For part a the p_v so then we can reject the null hypothesis at this significance level.

For part b the $p_v\alpha$ so then we FAIL to reject the null hypothesis at this significance level.

For part c the $p_v\alpha$ so again we FAIL to reject the null hypothesis at this significance level.

Answer from: Quest

answer: the four apples you took away.

step-by-step explanation:

Answer from: Quest

$4\left(625^4\right)\left(y^6\right)$

step-by-step explanation:

given expression is $4\sqrt{625^8y^{12}}$ .

now we need to simplify the given expression $\sqrt{20y^8}$ .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

$4\sqrt{625^8y^{12}}$

$=4\left(625^8y^{12}\right)^{\frac{1}{2}}$

$=4\left(625^8\right)^{\frac{1}{2}}\left(y^{12}\right)^{\frac{1}{2}}$

$=4\left(625^4\right)\left(y^6\right)$

expanding that will give a very very large number so let's keep answer in exponent form.

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For the hypothesis test h0: μ = 10 against h1: μ > 10 and variance known, calculate the pvalue...

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