ntroductory Video: Microsort(R) for Disease Prevention and Family Balancing http

Question

ntroductory Video: Microsort(R) for Disease Prevention and Family Balancing https://www.youtube.com/watch?v=7wzB1cSSVtQ Perform a hypothesis test using a 0.05 significance level to test Dr. Karabinus' claim (in the introductory video) about the success rate of the XSORT method of gender selection. Assume that the sample data that you are using consists of 55 girls born in 100 births. Part 1: What do we need to understand to construct a hypothesis test for Dr. Karabinus' claim? What values do we need to find to conduct a hypothesis test using a) the P-value method, b) the critical value method, and c) the confidence interval method? Part 2: Choose one of the three methods of hypothesis testing to test Dr. Karabinus' claim. Explain clearly how your hypothesis test is constructed and conducted without the use of technology. Show how the method works and give the meaning of the terminology in your own words. Part 3: Carefully word the final conclusion for your hypothesis test. Discuss the statistical significance of the results and your views regarding the use of gender selection methods?

Explanation / Answer

Part 1: What do we need to understand to construct a hypothesis test for Dr. Karabinus' claim? What values do we need to find to conduct a hypothesis test using a) the P-value method, b) the critical value method, and c) the confidence interval method?

Answer:

Dr. Karabinus’ claim that the proportion of girls is 50% and for checking this claim or hypothesis we need the values such as sample size n, number of successes x, the sample proportion P, and confidence level or significance level. Also, we need the critical value z for this testing of hypothesis.

Part 2: Choose one of the three methods of hypothesis testing to test Dr. Karabinus' claim. Explain clearly how your hypothesis test is constructed and conducted without the use of technology. Show how the method works and give the meaning of the terminology in your own words.

Answer:

Here, we have to use the z test for the population proportion.

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The population proportion for the girls is 0.50.

Alternative hypothesis: Ha: The population proportion for the girls is different than 0.50.

H0: p = 0.5 versus Ha: p 0.5

This is a two tailed test.

We assume the level of significance or alpha value as 5% or 0.05.

The test statistic formula is given as below:

Z = (P – p) / sqrt(pq/n)

Where, P is the sample proportion, p is the population proportion, n is the sample size and q = 1 – p

We are given,

Sample size n = 100,

Number of successes x = 55

Sample proportion = P = x/n = 55/100 = 0.55

Population proportion = p = 0.50

Now, we have q = 1 – p = 1 – 0.50 = 0.50

Now, plug all values in the above formula

Z = (0.55 – 0.50) / sqrt(0.50*0.50/100)

Z = 0.05/0.05

Test statistic = Z = 1.00

Critical values = -1.96 and 1.96

Test statistic value 1.00 is less than absolute critical value 1.96, so we do not reject the null hypothesis.

P-value = 0.3173

Alpha value = 0.05

P-value > Alpha value

So, we do not reject the null hypothesis that the population proportion for the girls is 0.50.

Part 3: Carefully word the final conclusion for your hypothesis test. Discuss the statistical significance of the results and your views regarding the use of gender selection methods?

Answer: We conclude that there is sufficient evidence that the population proportion for the girls is 50%. We can safely reject Dr. Karabinus' claim at 0.05 significance level about the success rate of the XSORT method of gender selection.

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