Question

Please show step by step work, thanks!

1. The CD4 T cell counts (x106/I) at baseline for a sample of 13 patients follows. 230 205 313 207 227 245 173 58 103 181 105 301 169 a) b)Determine a point estimate for the population mean CD4 T cell count. c) (assume the counts are normally distributed). d) (x 106 /1) . Based on the confidence interval from part (c), at a l0% significance level, do the sample data support this belief? Perform an appropriate hypothesis test Draw a boxplot of the data and comment on the skewness of the distribution. Determine a 90% confidence interval for the population mean CD4 T cell count Suppose researchers believe the average CD4 T cell count in the population is 210

Answer 1

a)

The data is skewed to the left

b) Point estimate for the mean is $\overline{x}=193.62$

$S=74.62$

c) $CI=\overline{x}\pm T_{\frac{\alpha }{2}}(\frac{S}{\sqrt{n}})$

For 90% confidence and df =n-1=13-1=12

$T_{\frac{\alpha }{2}}=1.7823$

$CI=193.62\pm 1.7823(\frac{74.62}{\sqrt{13}})$

$CI=193.62\pm 36.89\Rightarrow (156.73,230.51)$

d) 210 is within the confidence interval

Hence null hypothesis is not rejected