Significance level H1 0.01 0.05 0.02 0.01 Left Tailed –1.282 –1.645 –2.054 –2.32
ID: 3359423 • Letter: S
Question
Significance level
H1
0.01
0.05
0.02
0.01
Left Tailed
–1.282
–1.645
–2.054
–2.326
Right Tailed
1.282
1.645
2.054
2.326
Two Tailed
±1.645
±2.326
±2.326
±2.576
4. College tuition:The mean annual tuition and fees in the 2013–2014 academic year for a sample of 14 private colleges in California was $37,900 with a standard deviation of $7,200. A dotplot shows that it is reasonable to assume that the population is approximately normal. Can you conclude that the mean tuition and fees for private institutions in California differs from $35,000?
What is the null and alternative hypothesis?
Should a two-tailed, right-tailed, or left-tailed test be performed?
Calculate the P-value (Use T-Test on the TI Calculator and remember the P-value is p)
Round 3 decimals
Compare the P-value to =0.01 level of significance. Is the p-value less than, greater than, or equal to the level of significance = 0.01?
What is the result of the test? (Reject H0 or Do Not Reject H0)
State the conclusion.
Significance level
H1
0.01
0.05
0.02
0.01
Left Tailed
–1.282
–1.645
–2.054
–2.326
Right Tailed
1.282
1.645
2.054
2.326
Two Tailed
±1.645
±2.326
±2.326
±2.576
Explanation / Answer
Given that,
population mean(u)=35000
sample mean, x =37900
standard deviation, s =7200
number (n)=14
null, Ho: =35000
alternate, H1: !=35000
level of significance, = 0.01
from standard normal table, two tailed t /2 =3.012
since our test is two-tailed
reject Ho, if to < -3.012 OR if to > 3.012
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =37900-35000/(7200/sqrt(14))
to =1.5071
| to | =1.5071
critical value
the value of |t | with n-1 = 13 d.f is 3.012
we got |to| =1.5071 & | t | =3.012
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 1.5071 ) = 0.1557
hence value of p0.01 < 0.1557,here we do not reject Ho
ANSWERS
---------------
null, Ho: =35000
alternate, H1: !=35000
test statistic: 1.5071
critical value: -3.012 , 3.012
decision: do not reject Ho
p-value: 0.1557
we dont have evidence the mean tuition and fees for private institutions in California differs from $35,000
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