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alexdok [17]
3 years ago
10

A study was recently conducted to estimate the mean cholesterol for adult males over the age of 55 years. From a random sample o

f n10 ​men, the sample mean was found to be 242.6 and the sample standard deviation was 73.33. To find the 95 percent confidence interval estimate for the​ mean, what is the correct critical value to​ use?
Mathematics
1 answer:
Komok [63]3 years ago
8 0

Answer:  Correct critical value = 2.2622

Step-by-step explanation:

Confidence interval for population mean when population standard deviation is unknown:

\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}} , where \overline{x} = sample mean, n= sample size, s= sample standard deviation, t_{\alpha/2} = two-tailed t value.

As per given: n= 10

degree of freedom : df = n-1=9

\overline{x}=242.6\\\\s=73.33\\\\\alpha=5\%=0.05

Critical t-value : t_{\alpha/2,df}=t_{0.05/2,9}=t_{0.025,9}=2.2622

So, the 95 percent confidence interval estimate for the​ mean :

242.6\pm (2.2622)\dfrac{73.33}{\sqrt{10}}\\\\=242.6\pm (2.2622)(23.19)\\\\\approx242.6\pm52.46\\\\=(242.6-52.46,\ 242.6+52.46)\\\\=(190.14,\ 295.06)

The 95 percent confidence interval estimate for the​ mean:(190.14, 295.06)

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