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Lyrx [107]
2 years ago
5

What is the diameter of a sphere with a volume of 72 in”, to the nearest tenth of an inch?

Mathematics
1 answer:
GREYUIT [131]2 years ago
3 0

We know that,

Volume of sphere = 4/3πr³

72 = 4/3 × 22/7 × r³

72 × 21/88 = r³

³√17.18 = r

2.58 cm = r

:)

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For the hypothesis test H0: μ = 10 against H1: μ >10 and variance known, calculate the Pvalue for each of the following test
Basile [38]

Answer:

a) p_v =P(Z>2.05)=1-P(z

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

c) p_v =P(Z>0.4)=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(Z>2.05)=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(Z>0.4)=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.

3 0
3 years ago
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