Question

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? State hypotheses,

calculated value, critical value at a = 0.1

the professor wants to know wether the sample mean 67.57 is high enough.

Answer 1

We fail to reject the Null hypotheses that the average amount of money a typical college student spends per day is less than $70.

Step-by-step 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 <70`

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}{(\sigma)/(√(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 = (67.57-70)/((17.32)/(√(35) ) )\\\\z = (-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.