Question: Self-Reported and Measured Male Heights. As a part of the National Health and Nutrition Examination Survey conducted by the Department of Health and Human Services, self-reported heights and measured heights were obtained for males aged 12-16. Listed below are sample results.

Reported height     68    71       63    70     71     60     65     64     54     63     66     72

Measured height   67.9  69.9  64.9  68.3  70.3  60.6  64.5  67.0  55.6  74.2  65.0 70.8

1. Is there sufficient evidence to support the claim that there is a difference between self-reported heights and measured heights of males aged 13-16? Uses a 0.05 significance level.

   t-Test: Paired Two Sample for Means
   	Reported Height	Measured Height
   Mean	65.58333	66.58333
   Variance	27.90152	24.68879
   Observations	12	12
   Pearson Correlation	0.765888
   Hypothesized Mean Difference	0
   df	11
   t Stat	-0.98424
   P(T<=t) one-tail	0.173075
   t Critical one-tail	1.795884
   P(T<=t) two-tail	0.346149
   t Critical two-tail	2.200986

   
   The two tailed p-value is equal to p = 0.346149, which means that we fail to reject the null hypothesis.
2. Construct a 95% confidence interval estimate of the mean difference between reported heights and measured heights. Interpret the resulting confidence interval, and comment on the implications of whether the confidence interval limits contain 0.

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