R Markdown

According to “A Hundred Years Ago,” the benchmark height for women in 1912 was 63.75 inches tall. In a sample of 15 women from 1975, the mean height was 65 inches, with a sample standard deviation of 4.47 inches. Was the average height during 1975 different than it was in 1912 at a 5% significance level? HO: μ=63.75 HA: μ≠63.75

Code for t.test

t.test(women$height,alternative=("two.sided"),mu=63.75,conf.level=.95)
## 
##  One Sample t-test
## 
## data:  women$height
## t = 1.0825, df = 14, p-value = 0.2973
## alternative hypothesis: true mean is not equal to 63.75
## 95 percent confidence interval:
##  62.52341 67.47659
## sample estimates:
## mean of x 
##        65

Conclusion

We do not reject the null hypothesis, as the p-value of 0.297 is greater than the significance level of 5%, or 0.05. According to the data, from 1912 to 1975, the data suggests that the mean of women’s height in 1975 is not different from the historic average of 63.75 inches, in 1912.