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A study is conducted to test the hypothesis that people with glaucoma have higher than average blood pressure. The study includes 200 people with glaucoma whose mean systolic blood pressure, SBP, is 140 mm Hg with standard deviation of 25 mm Hg. (a) Construct and interpret a 95% confidence interval for the true mean SBP among people with glaucoma.

Respuesta :

Answer: The confidence interval would be (120.6, 159.4).

Step-by-step explanation:

Since we have given that

n = 200

mean = [tex]\bar{x}=140\ mm[/tex]

Standard deviation = [tex]\sigma=25\ mm[/tex]

At 95% confidence interval, z = 1.96

So, 95% confidence interval would be

[tex]\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=140\pm 1.96\times \dfrac{140}{\sqrt{200}}\\\\=140\pm 19.40\\\\=(140-19.4,140+19.4)\\\\=(120.6,159.4)[/tex]

Hence, the confidence interval would be (120.6, 159.4).

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