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3 years ago

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Mathematics

1 answer:

Sonbull [250]3 years ago

5 0

Answer:

A. 121 ⇒ III. 11

B. 64 ⇒ II. 4 and IV. 8

C. 27 ⇒ I. 3

D. 125 ⇒ V. 5

E. 16 ⇒ II. 4

Step-by-step explanation:

Let us find the correct answer

∵ 121 = 11 × 11

∴ The square root 121 is 11

∴ A. 121 ⇒ III. 11

∵ 64 = 8 × 8

∴ The square root of 64 is 8

∵ 64 = 4 × 4 × 4

∴ The cube root of 64 is 4

∴ B. 64 ⇒ II. 4 and IV. 8

∵ 27 = 3 × 3 × 3

∴ The cube root of 27 is 3

∴ C. 27 ⇒ I. 3

∵ 125 = 5 × 5 × 5

∴ The cube root of 125 is 5

∴ D. 125 ⇒ V. 5

∵ 16 = 4 × 4

∴ The square root of 16 is 4

∴ E. 16 ⇒ II. 4

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a) $z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649$

b) For this case we need to find a critical value that accumulates $\alpha/2$ of the area on each tail, we know that $\alpha=0.01$ , so then $\alpha/2 =0.005$ , using the normal standard table or excel we see that:

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Step-by-step explanation:

Data given and notation

n=420+174=594 represent the random sample taken

X=174 represent the number of yellow peas

$\hat p=\frac{174}{594}=0.293$ estimated proportion of yellow peas

$p_o=0.23$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of yellow peas is 0.23:

Null hypothesis: $p=0.23$

Alternative hypothesis: $p \neq 0.23$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>3.649)=0.00026$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

b) Critical value

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