Question

A professor of statistics claimed that the average amount of money a typical college

Answer 1

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.

$H_0= \mu$

For the given problem the Alternate hypotheses is that the average amount of money a typical college student spends per day is over $70.

$H_1= \mu >70$

The test statistic is given by

$z = \frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n} } }$

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.

$z = \frac{67.57-70}{\frac{17.32}{\sqrt{35} } }\\\\z = \frac{-2.43}{ 2.927}\\\\z = -0.83$

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.