# The Student Union claims that a population mean amount of spending of undergraduate students at the college is \$250 per trimester on textbooks with a population standard deviation of \$54. To test this...

The Student Union claims that a population mean amount of spending of undergraduate students at the college is \$250 per trimester on textbooks with a population standard deviation of \$54. To test this hypothesis, a random sample of 144 undergraduate students is polled and the amount each student spent on textbooks during the trimester is recorded. The sample mean is \$260 per trimester on textbooks.
REQUIRED: a) At the 0.05 level of significance, is there evidence that the population mean amount of spending is different from \$250 per trimester on textbooks? (3 marks)
At the 0.01 level of significance, is there evidence that the population mean amount of spending is different from \$250per trimester on Mks? (3 marks)

## Solution

David answered on Dec 20 2021
Q1
a.
H0: μ =250
H1: μ ≠ 250
The test statistic is z = ( 260-250)*144.5/54 = 2.22
with a 0.05 significance level and a two tail test the critical z value is 1.96
since the statistic value > critcal value we DO NOT ACCEPT the null hypothesis. There is no statistical evidence that mean spending in not \$250
.
H0: μ =250
H1: μ ≠ 250
The test statistic is z = ( 260-250)*144.5/54 = 2.22
with a 0.01 significance level and a two tail test the critical z value is 2.576
since the statistic value < critcal value we ACCEPT the null hypothesis. There is statistical evidence that mean spending is \$250.
c.
the diffrence in conclusions is due to the difference in type 1 e
or. this is the same as the...
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