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nikdorinn [45]
3 years ago
8

Can you help me find the test statistic AND Pvalue for a hypothesis test. The question is: In a survey respondents were asked wo

uld you be willing to pay higher taxes if the tax revenue went directly toward deficit reduction. Treat the respondents as a simple random sample of adults.
The survey results show


FEMALE MALE


Yes 33 30

No 65 72

Total 98 102
Mathematics
1 answer:
vitfil [10]3 years ago
8 0

Answer:

Test statistic z=0.65

P-value=0.52

Fail to reject the null hypothesis.

Step-by-step explanation:

Here we have to perform a hypothesis test on the difference of proportions. We may want to answer if there is significant difference in the proportions of male and females.

The null and alternative hypothesis are:

H_0: \pi_1=\pi_2\\\\H_1: \pi_1\neq\pi_2

The significance level is defined as 0.05.

The YES proportion for females is:

p_1=33/98=0.337

The YES proportion for males is:

p_2=30/102=0.294

The weighted average of p can be calculated as:

p=\frac{n_1*p_1+n_2*p_2}{n_1+n_2}=\frac{33+30}{98+102}=0.315

With this p, we estimate the standard deviation

s=\sqrt{\frac{p(1-p)}{n_1}+\frac{p(1-p)}{n_2} }=\sqrt{\frac{0.315(1-0.315)}{98}+\frac{0.315(1-0.315)}{102} }=0.066

The test statistic z can be calculated as:

z=\frac{p_1-p_2}{s} =\frac{0.337-0.294}{0.066}=\frac{0.043}{0.066}=0.65

We can calculate the p-value for z, taking into account is a two-sided test

P(|z|>0.65)=0.52

The P-value (0.52) is greater than the significance level (0.05), so the effect is not significant. It failed to reject the null hypothesis.

We have enough evidence to conclude that the proportions that vote YES are different between genres.

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Answer:

Replace w and z with the given values:

5^2 + 2 + 48 / 2(8)

Simplify:

75/16 = 4 and 11/16

Step-by-step explanation:

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Zepler [3.9K]

Answer:

a) \bar X=144.3

b) The 95% confidence interval would be given by (138.846;149.754)      

c) n=34

d) n=298

e) n=1190

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the sample mean with this formula:

\bar X = \frac{\sum_{i=1}^n x_i}{n}

\bar X=144.3 represent the sample mean  

\mu population mean (variable of interest)

\sigma=8.8 represent the population standard deviation

n=10 represent the sample size  

a) Find a point estimate of the population mean

We can calculate the sample mean with this formula:

\bar X = \frac{\sum_{i=1}^n x_i}{n}

\bar X=144.3

b) Construct a 95% confidence interval for the true mean score for this population.

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that t_{\alpha/2}=1.96

Now we have everything in order to replace into formula (1):

144.3-1.96\frac{8.8}{\sqrt{10}}=138.846    

144.3+1.96\frac{8.8}{\sqrt{10}}=149.754

So on this case the 95% confidence interval would be given by (138.846;149.754)    

Part c

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =+20 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got z_{\alpha/2}=1.960, replacing into formula (5) we got:

n=(\frac{1.960(8.8)}{3})^2 =33.05 \approx 34

So the answer for this case would be n=34 rounded up to the nearest integer

Part d

n=(\frac{1.960(8.8)}{1})^2 =297.493 \approx 298

So the answer for this case would be n=298 rounded up to the nearest integer

Part e

n=(\frac{1.960(8.8)}{0.5})^2 =1189.97 \approx 1190

So the answer for this case would be n=1190 rounded up to the nearest integer

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