Respuesta :
The required results are following:
Step O : 1) Yes ,
2) Yes ; 3) No
step 1 : The null and alternative hypothesis are
H₀ : p = 0.105
Hₐ : p < 0.105
Step 2 : test statistic value is -0.865.
Step 3 : p- value is 0.1935 > 0.01 (α)
So, Fail to Reject null hypothesis and No, evidence to support that probability of births to mothers under 20 years of age is decreasing.
We have given that A sociologist claim that Births to mothers under 20 years of age is decreasing in United States.
Given data in statistics terms are
Sample size (n) = 134
Number of success = 11
level of significance , α = 0.01
hypothetical population proportion, p₀= 0.105
Step 0 :
1. Yes, this is a simple random sample because it fulfill all requirements.
2. Yes
np₀(1 - p₀) > 10
=> 134 x 0.105(1 – 0.105) > 10
=> 12.59265 > 10
3. No, as N is not given.
Step 1 :
The null and alternative hypothesis are
H₀: p = 0.105
Hₐ : p < 0.105
This is left-tailed hypothesis test.
Step 2:
The value of sample proportion (p-hat) = 11/134
The value of test statistic is
Z= (p-hat - p₀ )/√p₀(l-p₀)/n
Z = (11 /134 - 0.105)/√0.105(1-0.105) 134
Z= - 0.86512688616
Z = -0.865
Step 3 :
α =0.01 , Zα=-2.326
No, The test statistic does not lie in the rejection region
The P-value is
P-value= P(Z < z )
P-value= P(Z < -0.865 )
P-value= P(Z< -0.865)
P-value= 0.193519
P-value= 0.1935 > 0.01
Fails to Reject null hypothesis because P-value (0.1935) is greater than level of significance (0.01).
No, there is not sufficient evidence to conclude that the percentage of live births to mother under age 20 years of age in the United States has decreased below the 2006 level of 10.5%.
To learn more about Left tailed hypothesis test , refer:
https://brainly.com/question/28590902
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Complete question:
In 2006, 10.5% of all live births in the United States were to mothers under 20 years of age. A sociologist claims that births to mothers under 20 years of age is decreasing. She conducts a simple random sample of 134 births and finds that 11 of them were to mothers under 20 years of age. Test the sociologist's claim at the a = 0.01 level of significance. Answer:
Step O: Verify Assumptions 1. Is this a simple random sample? (yes, no) 2. Is np. (1 - p.) > 10 ? (yes, no) 3. Is n < 0.05N? (yes, no)
Step 1: Parameter of interest: II.:P versus :p
Step 2: Test statistic: Sample Proportion= (Write your answer as a fraction without simplifying) Z. - (Use the value of the sample proportion as a fraction without simplifying in the formula of the test statistic and round your test statistic for three decimal places)
Step 3: Classical approach Z = (Rounded to three decimal places) Does the test statistic lie in the rejection region? (yes, no)
Step 4: p-value approach p-value= (Rounded to four decimal places) What is the relationship between p-value and a? p-value a. (>,<)
Step 5: Conclusion: Is there sufficient evidence to conclude that the percentage of live births to mothers under age 20 years of age in the United States has decreased below the 2006 level of 10.5%? (yes, no)
