Problem 35, page 376: One way doctors try to determine how long a single dose of

Question

Problem 35, page 376: One way doctors try to determine how long a single dose of pain-reliever will provide relief is to measure the drug's half-life, which is the length of time it takes for one half of the dose to be eliminated from the body. The following table provides the half-lives of the pain reliever oxycodone for a sample of 18 individuals: 3.3 4.7 1 2.0 2.5 3.7 4.3 5.0 1.2 6.0 2.8 3.9 3.5 2.1 4.8 3.0 4.9 a) Check for normality: Are there any outliers? b) Construct a 95% confidence interval for this sample c) The NIH report that the mean half-life for Oxycodone is 3.51, does this sample contradict this mean number? d) Would it be surprising if a sample mean from a different sample showed a mean of about 4.5 hours?

Explanation / Answer

Part a

We know that if the value is below 1.5*IQR from Q1 or above 1.5*IQR from Q3, then this value considered as an outlier.

For the given variable X, we have following descriptive statistics:

Variable             N       Mean     Median     TrMean      StDev    SE Mean

X                   18      3.583      3.600      3.581      1.359      0.320

Variable       Minimum    Maximum         Q1         Q3

X                1.200      6.000      2.400      4.825

IQR = Q3 – Q1 = 4.825 – 2.4 = 2.425

1.5*IQR = 1.5*2.425 = 3.6375

Q1 - 1.5*IQR = 2.4 - 3.6375 = -1.2375

Q3 + 1.5*IQR = 4.825 + 3.6375 = 8.4625

All values are lies within -1.2375 and 8.4625, so there is no any outlier.

Part b

Now, we have to find 95% confidence interval.

Confidence interval = Xbar -/+ t*S/sqrt(n)

We are given

Xbar = 3.583

S = 1.359

n = 18

df = n – 1 = 18 – 1 = 17

Confidence level = 95%

Critical t value = 2.1098

(By using t-table or excel)

Confidence interval = 3.583 -/+ 2.1098*1.359/sqrt(18)

Confidence interval = 3.583 -/+ 2.1098* 0.320319372

Confidence interval = 3.583 -/+ 0.6758

Lower limit = 3.583 - 0.6758 = 2.9072

Upper limit = 3.583 + 0.6758 = 4.2588

Confidence interval = (2.9072, 4.2588)

Part c

This sample does not contradict the given mean number 3.51, because it is lies within given confidence interval.

Part d

Yes, it would be surprising if a sample mean from a different sample showed a mean of about 4.5 hours, because the value 4.5 is not lies within given confidence interval.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.