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

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