A 0.05 significance level is used for a hypothesis test of the claim that when parents use a particular method of genderselection, the proportion of baby girls is less than 0.5. Assume that sample data consists of 66 girls in 144 births, so the sample statistic of 11/ 24 EndFraction 11 24 results in a z score that is 1 standard deviation below 0. a) what is the pvalue b) critic value c) area of the critical region

a) P-value=0.16

b) critic value zc=-1.645

c) area of the critical region = 0.05

Step-by-step explanation:

We have a hypothesis test on the population proportion.

The sample proportion is p=66/144=11/24=0.4583.

The z-statistic results in z=-1.

As the alternative hypothesis (the claim) states that the proportion is below 0.5, the test is left-tailed.

The P-value for this type of test and with a z=-1 is calculated as:

The critial value depends on the significance level. In this test we have a significance level of 0.05.

The critical value can be looked-up in a standard normal distribution table. Its the value for which the probability of having a statistic below this critical value is equal to the significance level (0.05):

For this test, the critical value is zc=-1.645.

As the área of the critical region is equal to the probability of having a statistic below this critical value, and this is the significance level, we have a área of the critical region equal to 0.05.

a)

Since is a left tailed test the p value would be:  

b)

c) For this case since is a left tailed test the critical region or the rejection zone of the null hypothesis would be:

Step-by-step explanation:

Data given and notation

n=144 represent the random sample taken

X=66 represent the number of girls

estimated proportion of girls

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

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 true proportion is less than 0.5.:  

Null hypothesis:  

Alternative hypothesis:  

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

(1)  

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

Calculate the statistic  

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

Part a : p value

The significance level provided . The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

Part b

We want to conduct a left tailed test with and we need to find a critical value in the normal standard distribution who accumulates 0.05 of the area in the left and we got:

Part c

For this case since is a left tailed test the critical region or the rejection zone of the null hypothesis would be:

b

step-by-step explanation:

calculate the scale factor as the ratio of corresponding sides, image to original, that is

scale factor = = = = 1