(2) Collect 50 or more quantitative data items. Use the same method of collectin

Question

(2) Collect 50 or more quantitative data items. Use the same method of collecting 50 or more data items that you used in the Module 1 discussion. You may even use the same data you used in Modules 1, 2, or 6. You will first construct an appropriate set of hypotheses, H0 and H1, regarding your data. This might involve doing research regarding your data beforehand to figure out a meaningful set of hypotheses.

View an example on how to use StatCrunch (with data) to do hypotheses tests for a population mean.

Then, answer the following five parts:

Write down the null hypothesis.

Write down the alternative hypothesis.

Explain why you chose your hypotheses as such.

Do a hypothesis test of your data at the = 2% level of significance for the population mean by carrying out the following six steps:

Write down the degrees of freedom, n-1.

View an example on how to use StatCrunch to compute the value t
If it is left-tailed test, what is the critical value, -t0.02?
If it is right-tailed test, what is the critical value, t0.02?
If it is two-tailed test, what are the two critical values, ±t0.01?

Write down the test statistic, t0.

Write down the P-value.

Write down the sample size.

Write down the sample mean and sample standard deviation.

Use the classical method to reach your conclusion on whether or not to accept or reject the null hypothesis. Be sure to explain how you reached your conclusion.

Use the P-value to reach your conclusion on whether or not to accept or reject the null hypothesis. Be sure to explain how you reached your conclusion.

Does the conclusion make sense to you? Why, or why not?

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Explanation / Answer

Answer to the question)

we got 50 data values of blood group of people

There are four major types of blood groups , and o is the most common of them

Thus we can conduct a research to test the claim that o is the most common blood group of all

which would be mean that the proportion of O would be more than 25%

Thus the null hypothesis is: The proportion of people with blood group O is 25% or 0.25

Alternate hypothesis is: The proportion of peopl with blood group O is more than 25% or 0.25

.

The explanation why this hypothesis is chosen is provided above, because it is a claim that O is the most common blood group which implies majority of people must be having this blood group. 25% is the value chosen based on the fact that there are 4 types of blood groups and if all four have equal chances the proportion of each blood group woudl be 25%. But since the claim says O is more popular , we expect the blood group O to have a proprtion value greater than 25%

The sample size is n = 60

degree of freedom (df) = n - 1 = 60-1 = 59

.

The T critical values for for 0.02 alpha , df = 59 , right tailed test would be :

We get T critical = 2.1002

.

from the data we get that there are 28 out of 60 respondents with blood group O

Sample proportion P^ = 28 /60 = 0.4667

.

The formula of test statistic is:

t = (p^-p) / sqrt(p*(1-p)/n)

t = (0.4667-0.25) / sqrt(0.25*0.75/60)

t = 3.87645

.

P value for df = 59 , right tailed test , t = 3.87645 is

P value = 0.000134

.

Conclusion: Since the P value 0.000134 < alpha 0.02 , we reject the null hypothesis

and conclude that there is significant evidence to support the claim that the proportion of O is greater than 25%

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