A new chemical has been found to be present in the human blood stream, and a med

Question

A new chemical has been found to be present in the human blood stream, and a medical group would like to study the presence of this chemical in some samples of patients. The presence of the chemical in a patient is measured by a score representing the 'parts per billion' in which that chemical appears in the blood. It is known that, on this scale, men have an average score of 816.8 and a standard deviation of 54. It is also known that women have an average score of 839.3 and a standard deviation of 24. An assistant in the medical team has been handed a sample of 100 scores. The assistant knows that all of the scores are from one of the two genders, but the sample was not documented very well and so they do not which gender this is. Within the sample, the mean score is 829.22. a)

Complete the following statements. Give your answers to 1 decimal place. If the sample came from a group of 100 men, then the sample mean is_____ standard deviations above the mean of the sampling distribution. In contrast, if the sample came from a group of 100 women, then the sample mean______ is standard deviations below the mean of the sampling distribution.

b)Based on this, the assistant is more confident that the sample came from a group of 100 men or women

Explanation / Answer

for z score is measure of relative distance of an obserrvation from mean

also z score=(X-mean)/std deviation

. If the sample came from a group of 100 men, then the sample mean is (829.22-816.8)/54 =0.23  standard deviations above the mean of the sampling distribution. In contrast, if the sample came from a group of 100 women, then the sample mean (829.22-839.3)/24=0.42   is standard deviations below the mean of the sampling distribution.

b)

as z score of 0.23 is closer to mean of std deviation(0) ; therefore  assistant is more confident that the sample came from a group of 100 men

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