# 8.14 test for a significant difference in the variances of the

**8.14 Test for a significant difference in the variances of the initial white blood cell count between patients who did and patients who did not receive a bacterial culture.**

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**8.15 What is the appropriate test procedure to test for significant differences in mean white blood cell count between people who do and people who do not receive a bacterial culture?**

**8.18 Compute a 95% CI for the true difference in mean white blood cell count between the two groups.**

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**A 1980 study was conducted whose purpose was to compare the indoor air quality in offices where smoking was permitted with that in offices where smoking was not permitted [7]. Measurements were made of carbon monoxide (CO) at 1:20 p.m. in 40 work areas where smoking was permitted and in 40 work areas where smoking was not permitted. Where smoking was permitted, the mean CO level was 11.6 parts per million (ppm) and the standard deviation CO was 7.3 ppm. Where smoking was not permitted, the mean CO was 6.9 ppm and the standard deviation CO was 2.7 ppm.**

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**a) ****State the null hypothesis**

*Null hypothesis: There is no significant difference between the mean CO level in institutions where smoking is permitted and institutions where smoking is not permitted. *

**b) ****State the alternative hypotheses **

*There is a significant difference between the mean CO level in institutions where smoking is permitted and institutions where smoking is not permitted. *

c) show the test statistics.

**Work areas (1)=40**

**Work areas 2=40**

**Standard deviation of work area 1= 11.6**

**Standard deviation of work area 2= 2.7**

**Mean of work area 2= 6.9**

**Mean of work area 1= 7.3**

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**Ho= standard dev1=standard dev2**

**Ha= standard dev1 does not equal standard dev 2**

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**F test: standard deviation of work area 1^2 / standard deviation of work area 2**

**7.3^2/2.7^2**

**7.31**

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**DOF= 40-1=39 ( for both)**

**Critical value = .05**

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8.25 Test for whether the standard deviation of CO is significantly different in the two types of working environments.

A camera has been developed to detect the presence of cataract more accurately. Using this camera, the gray level of each point (or pixel) in the lens of a human eye can be characterized into 256 gradations, where a gray level of 1 represents black and a gray level of 256 represents white. To test the camera, photographs were taken of 6 randomly selected normal eyes and 6 randomly selected cataractous eyes (the two groups consist of different people). The median gray level of each eye was computed over the 10,000+ pixels in the lens. The data are given in Table 8.14.

8.28 What statistical procedure can be used to test whether there is a significant difference in the median gray levels between cataractous and normal eyes?

* paired t test?

8.29 Carry out the test procedure mentioned in Problem 8.28, and report a p-value.

8.30 Provide a 99% CI for the mean difference in median gray levels between cataractous and normal eyes.

8.39 What is the appropriate test procedure to determine whether there is a systematic difference between the assessments of Doctor A vs. Doctor B?

? chi squared analysis?

* appropriate statistical procedure

* why?

8.56 What test can be performed to compare the variances of the two genotype groups?

8.92 What test can be used to compare the mean ln (ERG amplitude) between patients with dominant vs. recessive RP?