Respuesta :
Answer:
We fail to reject the Null hypotheses that the average amount of money a typical college student spends per day is less than $70.
Explanation:
A professor of statistics claimed that the average amount of money a typical college student spends per day during social distancing at home is over $70.
Based upon previous research, the population standard deviation is estimated to be $17.32.
The professor surveys 35 students and finds that the mean spending is $67.57.
Is there evidence that the average amount spent by students is less than $70?
For the given problem the Null hypotheses is that the average amount of money a typical college student spends per day is less than $70.
[tex]H_0= \mu <70[/tex]
For the given problem the Alternate hypotheses is that the average amount of money a typical college student spends per day is over $70.
[tex]H_1= \mu >70[/tex]
The test statistic is given by
[tex]z = \frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
Where X_bar is the sample mean spending that is $67.57, μ is the average population spending that is $70, σ is the standard deviation that is 17.32 and n is the sample size that is 35.
[tex]z = \frac{67.57-70}{\frac{17.32}{\sqrt{35} } }\\\\z = \frac{-2.43}{ 2.927}\\\\z = -0.83[/tex]
The p-value corresponding to the z-score of -0.83 at significance level 0.10 is found to be
p-value = 0.2036
Since 0.2036 > 0.10
We fail to reject the Null hypotheses that the average amount of money a typical college student spends per day is less than $70.
