In 1960, census results indicated that the age at which American men first marri
ID: 3227786 • Letter: I
Question
In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased during the past 40 years. A random sample of 40 men was observed. The men in our sample married at an average age of 24.2 years, with a standard deviation of 5.3 years. Is this enough evidence to suggest that the average age that a man gets married is greater than 23.3 years?
a. Write out the null and alternative hypothesis. b. Check all assumptions. c. Find the test statistic and the p-value. d. Compare the p-value to the significance level. What is your conclusion? e. Find and interpret an appropriate confidence interval for the true population mean , even if you do NOT have a statistically significant result.
Explanation / Answer
null hypothesis: Ho: mean <=23.3
alternate hypothesis: mean>23.3
b)as as sample size is random in nature and size>30 we can assume it to be normally distributed
c) std error of mean =std deviation/(n)1/2 =0.838
hence test stat t=(X-mean)/std error =(24.2-23.3)/0.838 =1.074
p value =0.1447
d)as p value is higher then 0.05 level we can not reject null hypothesis
e)for 95% CI, t=2.0227
hence 95% confidence interval =sample mean -/+z*Std error =22.505 ; 25.985
above interval gives 95% chance to contain tru population mean age of getting married