Question

One of the most important factors in blood coagulation and clot formation in humans is a protein called prothrombin, which must be converted into the enzyme thrombin in order for coagulation to occur. A random sample was taken from a population with a vitamin K deficiency (typically a population that has a low prothrombin level) and the results are given below, measured in mgdL:

S={18.70,19.45,23.40,21.8,19.54,22.19,20.14,20.37,23.02,19.46,18.98}

It is known that the population standard deviation prothrombin levels of a population is about 10.98 mgdL.

a)What is a point estimate for the mean prothrombin level for the population of interest? Round to 2 decimal places (for this problem only, use exact value for all other calculations).

b)What is the appropriate critical value for an associated two-sided 92% confidence interval? Round to 2 decimal places. (Use this for other calculations)

c)What is the marginal error associated to a 92% confidence interval for this study? (Round to 2 decimal places)

d)

What is the 92% confidence interval for the population mean prothrombin levels for the population of interest? (least to greatest, round to 2 decimal places)

(   ,   )

e)For a 92% level of confidence, what is the level of statistical significance for any hypothesis test conducted with it? (Give answer as a decimal)

Answer 1

using excel>addin>phstat>confidence interval

we have

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	10.98
Sample Mean	20.64090909
Sample Size	11
Confidence Level	92%
Intermediate Calculations
Standard Error of the Mean	3.310594563
Z Value	1.75068607
Margin of Error	5.79581179
Confidence Interval
Interval Lower Limit	14.8450973
Interval Upper Limit	26.43672088

a)the point estimate for the mean prothrombin level for the population of interest is 20.64

b)the appropriate critical value for an associated two-sided 92% confidence interval is 1.75

c) the marginal error associated to a 92% confidence interval for this study is 5.80

d)the 92% confidence interval for the population mean prothrombin levels for the population of interest

( 14.85 , 26.44 )

e) the level of statistical significance is 0.08