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.

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.

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

The test statistic is given by

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.

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.

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