dr. back is a successful chiropractor who needs to treat on average at least 90

Question

dr. back is a successful chiropractor who needs to treat on average at least 90 patients a week to meet his financial goals for his business. data was collected during 18 randomly selected week. The sample mean was 100.3 patients treated per week with a sample standard deviation,s, equal to 16.6 patients treated per week. with a 95% confidence level, can be concluded that:

A. Dr.Back is seeing between 50.3 to 87.2 patients per week, therefore his financial goals are not being met.

B. Dr.Back is seeing between 92.03 to 108.67 patients per week, therefore his financial goals are being met.

C. Dr.Back is seeing between 100.3 to 118.57 patients per week, therefore his financial goals are being met.

D. Dr.Back is seeing between 77.33 to 82.03 patients per week, therefore his financial goals are not being met.

Explanation / Answer

We need to find Confiedance interval with 95% confiedance level

Population Mean=Sample Mean+/-Sample Error

=100.3+/-(t*sd/sqrt(n-1))

To find the t vlaue we need to look into t table for where we have degree of freedom (df)=17 and column we look for is 95%( Use 2 tail confiedance interval for column )

t=2.1098

Population Mean=100.3+/-(2.1098*16.6/sqrt(17))= either 92.04 and 108.55

Hence Our population mean lies in between (92.03 and 108.67) as both ends are above 90 patients per week therefore Dr. Back can achieve his financial goals

Option B is correct

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