## Transcribed Text

1
Hypothesis testing
*Use the 5% level of significance for all the following tests.
1. Hypothesis testing for
when
2
is known.
a)
A random sample of size 100 is taken and
X
=8. Test
H0
.
*Use z-score because sample size is large, this is a two-tail test.
b)
A random sample of size 100 is taken and
X
=10.5. Test
H0
.
*This is a one-tail test.
2. Hypothesis testing for
when
2
is unknown (we can only calculate
2
s
from the
sample).
A random sample of size 36 is taken. The sample mean is 148 and the sample variance is 81.
Test
H0
*Sample size is small so use t-score
2
3. Hypothesis testing for
when
2
is unknown, and the sample size is small.
The current rate for producing 5 amp fuses at Neary Electric Co. is 250 per hour on average. A
new machine has been purchased and installed. According to the supplier, it will increase the
production rate. A sample of 10 randomly selected hours from last month production reports the
following production numbers: 245, 254, 259, 240, 257, 280, 258, 278, 290 and 241 fuses per
hour.
*This is a one tail test.
1) Calculate sample mean;
2) Calculate sample standard deviation;
3) Calculate standard error;
4) Based on above information, perform a hypothesis test that answers the following question: At
the .05 significance level can Neary conclude that the new machine is faster than 250 per hour?
4. We ran a regression on college GPA using high school GPA as the only independent
variable. The coefficient for high school GPA and its standard error are reported in the
table below (ignore the intercept; n=141).
Coefficients
Standard
Error
Intercept 1.415434 0.306938
hsGPA 0.482435 0.089826
a) At .05 level, test the hypothesis that the coefficient of ‘hsGPA’ is equal to ‘0’. Can you
reject or not reject the null? Show your steps.
*This is a two-tail test.
b) At .01 level, test the hypothesis that the coefficient of ‘hsGPA’ is positive (greater than
‘0’). Can you reject or not reject the null? Show your steps.
*This is a one-tail test.
c) What can you conclude from above hypotheses testing results?

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