Question

The National Center for Education Statistics found that in 2015, 41% of students nationwide reported that their mothers had graduated from college. A superintendent randomly sampled 356 students from her local school district and found that 43% of them had mothers that graduated from college. Does her sample give evidence of a higher education level among mothers in her district? Use a significance level of ? = 0.05.

a) State the hypotheses in symbols.   

b) Run the test and report the test statistic and p-value. Be sure to write out what you entered in your calculator.

c) Write a full conclusion for this test in the context of the problem (see #2b for format).   

d) Find a 90% confidence interval for the proportion of students in the superintendent’s district that have mothers who graduated from college. Be sure to write out what you entered in your calculator.

e) Does this confidence interval support your conclusion in part (c)? Explain.

Answer 1

Given : Sample size=n=356 , Sample proportion=p=0.43 , Population proportion=p0=0.41 , Sifnigicance level=0.05

a) Hypothesis : Vs

b) The test statistic is ,

The p-value is ,

p-value=

; From standard normal distribution table

(c) Decision : Here , p-value >0.05

Therefore , fail to reject Ho.

Conclusion : Hence , the sample does not give evidence of a higher education level among mothers in her district.

(d) The 90% confidence interval for the proportion of students in the superintendent’s district that have mothers who graduated from college is ,

;

(e) Decision : Here , the value 0.41 lies in the confidece interval.

Therefore , fail to reject Ho

Therefore , confidence interval support your conclusion in part (c).