 # The time a patient must wait before being attended by a physician in a hospital sodni3 2021-10-23 Answered
The time a patient must wait before being attended by a physician in a hospital has been observed for each of 100 randomly selected patients he sample mean is 70.3 minutes and the standard deviation is 28.2 minutes. Test the hypothesis that the mean waiting time in the hospital is not more than 65 minutes.
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Step 1
Hypothesis Testing:
It is basically a comparison of the statistical measures of the data with one sample(population) or two samples(populations) or more than two samples(populations). There are two hypotheses namely NULL and ALTERNATIVE.
The tail of the hypothesis will be decided from the alternative hypothesis. If it is '<' then left tail; '>' then right tail; $\text{Undefined control sequence \displaystylenene}$ then two-tail. Whereas the null hypothesis is almost $=0$ in most of the cases.
As the sample size is more than 30, the testing of the hypothesis is Z-test.
One-Sample Z-Test:
It is the hypothesis testing done for comparing the mean of the data to a specific value. As the name says it is a one-sample t-test, the data of one sample is considered for the complete hypothesis testing and the test statistics will be found from that data.
Step 2
Here,
The level of significance is not mentioned so, it is considered to be the commonly used level of significance, that is $\alpha =0.05$.
${H}_{0}:\stackrel{―}{X}=65VS{H}_{a}:\stackrel{―}{X}\le 65$
The test statistics $Z=\frac{\stackrel{―}{X}-{\mu }_{0}}{\frac{\sigma }{\sqrt{n}}}$
$Z=\frac{65-70.3}{\frac{28.2}{\sqrt{100}}}$
$=\frac{-5.3}{\frac{28.2}{10}}$
$=-1.8794326241$
$\stackrel{\sim }{=}-1.8794$
Step 3
The P-value of the Test statistics is
$P\left(|Z|\le |-1.87943|\right)=0.030093$.
The P-value is less than the level of significance, $0.03<0.05$.
Therefore, there is sufficient evidence to reject the null hypothesis.
The mean waiting time in the hospital is less than 65 minutes. That is, the mean waiting time in the hospital is not more than 65 minutes.