IHP 525 Module Six Problem Set PDF

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IHP 525 Module Six Problem Set Nicole Tassello

µ1, µ2, σ1 H0: Ha: x 1. Hemoglobin levels in 11-year-old boys vary according to a normal distribution with σ=1.2 g/dL. a) How large a sample is needed to estimate µ with 95% confidence so the margin of error is no greater than 0.5 g/dL? n= (z1-a/2 • σ/m)

n=(1.96 • 1.2/0.5)2 =22.13

A sample of 23 boys would be needed. 2. A researcher fails to find a significant difference in mean blood pressure in 36 matched pairs. The test was carried out with a power of 85%. Assuming that this study was well designed and carried out properly, do you believe that there really is no significant difference in blood pressure? Explain your answer. A test carried out with 85% power (assuming appropriate and accurate calculations and designs) would be expected to have an 85% chance of ending up with a p-value of less than 5%, which means results would be statistically significant. For tests, it is typical to strive for atleast 80% power, which this test exceeds. Since it is likely that the researcher would have found statistically significant data if it existed, failure to find this data suggests to maintain H0 and there was no significant difference in blood pressure in this study.

3. Would you use a one-sample, paired-sample, or independent-sample t-test in the following situations? a) A lab technician obtains a specimen of known concentration from a reference lab. He/she tests the specimen 10 times using an assay kit and compares the calculated mean to that of the known standard. One Sample t-test b) A different technician compares the concentration of 10 specimens using 2 different assay kits. Ten measurements (1 on each specimen) are taken with each kit. Results are then compared. Paired Sample t-test

4. In a study of maternal cigarette smoking and bone density in newborns, 77 infants of mothers who smoked had a mean bone mineral content of 0.098 g/cm3 (s1 = 0.026 g/cm3). The 161 infants whose mothers did not smoke had a mean bone mineral content of 0.095 g/cm3 (s2 = 0.025 g/cm3). a) Calculate the 95% confidence interval for µ1 - µ2. n1 = 77 x 1= 0.098 g/cm3 s1= 0.026 g/cm3

n2 = 161 x 2= 0.095 g/cm3 s2= 0.025 g/cm3

df=n-1= 76 (use 60)

SEx1-x1=√(0.026)2 + (0.025)2 = 0.003558 77 161 ( x 1 - x2) ± tdf1-a/2 x SEx1-x2 = (0.098-0.095) ± (2)(0.003558) = 0.003 ± 0.007116 The confidence interval at 95% is from -0.004 to 0.01.

b) Based on the confidence interval you just calculated, is there a statistically significant difference in bone mineral content between newborns with mothers who did smoke and newborns with mothers who did not smoke? Assuming H0: µ1-µ2=0, at the 95% confidence interval, there is no statistic significance since 0 is included in the confidence interval. Retain H0.

5. A randomized, double-blind, placebo-controlled study evaluated the effect of the herbal remedy Echinacea purpurea in treating upper respiratory tract infections in 2- to 11-year olds. Each time a child had an upper respiratory tract infection, treatment with either echinacea or a placebo was given for the duration of the illness. One of the outcomes studied was “severity of symptoms.” A severity scale based on four symptoms was monitored and recorded by the parents of subjects for each instance of upper respiratory infection. The peak severity of symptoms in the 337 cases treated with echinacea had a mean score of 6.0 (standard deviation 2.3). The peak severity of symptoms in the placebo group (np = 370) had a mean score of 6.1 (standard deviation 2.4). Test the mean difference for significance using an independent t-test. Discuss your findings. n1 = 337 x 1= 6 s1= 2.3

n2 = 370 x 2= 6.1 s2= 2.4

A) H0: µ1= µ2 Ha: µ1 ≠ µ2

B) df=337-1=336 (use 100)

tstat= 6 - 6.1 .= -0.1/0.1765 = 0.5656 √(2.3)2 + (2.4)2 337 370 The mean difference in this test is not statistically significant. Looking at the Table C in the textbook, we can see that t=0.5656 has a tail probability of less than 0.5, which means it falls in a less than 50% confidence interval. H0 would be retained....