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Alexeev081 [22]
3 years ago
14

A researcher has two percentages and wants to know if the percentages are statistically different. The researcher calculates the

z value and finds that it is 4.21. This means that the two percentages: A) Are the same. B) Are not statistically different. C) Have a 421 percent chance of not being different. D) Are statistically different.
Mathematics
1 answer:
love history [14]3 years ago
4 0

Answer:

p_v =2*P(Z>4.21) =2.55x10^{-5}

And we can use the following excel code to find it:"=2*(1-NORM.DIST(4.21,0,1,TRUE)) "

With the p value obtained and using the significance level assumed for example\alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the percentage 1 is significantly different from the percentage 2.

D) Are statistically different.

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis: \mu_1 = \mu_2  

Alternative hypothesis: \mu_1 \neq \mu_2  

Or equivalently:  

Null hypothesis: \mu_1 - \mu_2 = 0  

Alternative hypothesis: \mu_1 -\mu_2\neq 0  

Where \mu_1 and \mu_2 represent the percentages that we want to test on this case.

The statistic calculated is on this case was Z=4.21. Since we are conducting a two tailed test the p value can be founded on this way.

p_v =2*P(Z>4.21) =2.55x10^{-5}

And we can use the following excel code to find it:"=2*(1-NORM.DIST(4.21,0,1,TRUE)) "

With the p value obtained and using the significance level assumed for example\alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the percentage 1 is significantly different from the percentage 2.

And the best option on this case would be:

 D) Are statistically different.

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