SOLUTION: 1 The hospital records show that the mean weight of newly born baby is 7 lbs, with the standard deviation of 0.75 lbs. A researcher takes a sample of 55 newly born babies and foun

Question 75072: 1 The hospital records show that the mean weight of newly born baby is 7 lbs, with the standard deviation of 0.75 lbs. A researcher takes a sample of 55 newly born babies and found to have a mean weight of 6.73 lbs. Test the claim at 0.05 level of significance.(use z-test)
2 To compare freshmen�s knowledge of mathematics in two departments of the College of Computer of the Manuel S. Enverga University Foundation, a certain professor in business mathematics got a sample of economics and accountancy students and gave them special examination. A sample of 25 economics major students had a mean score of 85.85 with standard deviation of 7.5. A sample of 29 accounting major students had a mean score of 90.5 with a standard deviation of 10.3. Is there a significant difference between the two sample means? Use 0.01 level of significance.(use t-test)
3 In the contest of Search for Most Outstanding Teacher, 3 candidates are teaching Mathematics, 2 are teaching English, 2 are teaching Science and 1 teaching Filipino. What is the probability that the winner is teaching:
a.Mathematics
b.Science
c.Filipino
d.Any subject except English
e.Any subject except Math
4) If the probabilities are 0.40, 0.55 and 0.3 that student will get a failing grade either in Accountancy or Marketing, or in both, what is the probability that he fail at least one of these subjects?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1 The hospital records show that the mean weight of newly born baby is 7 lbs, with the standard deviation of 0.75 lbs. A researcher takes a sample of 55 newly born babies and found to have a mean weight of 6.73 lbs. Test the claim at 0.05 level of significance.(use z-test)
-------
Ho: u=7 lbs
Ha: u is not equal 7 lbs
------------
z(6.73)=(6.73-7)/0.75/sqrt55=-2.6698
The test is two tail so the p value
associated with z=-2.6698 is 0.00379*2=0.007589
The critical value of alpha = +/-1.96
Conclusion:
Reject Ho since p value<5%
Mean weight is not 7 lbs.
========
Cheers,
Stan H.
======================================

2 To compare freshmen�s knowledge of mathematics in two departments of the College of Computer of the Manuel S. Enverga University Foundation, a certain professor in business mathematics got a sample of economics and accountancy students and gave them special examination. A sample of 25 economics major students had a mean score of 85.85 with standard deviation of 7.5. A sample of 29 accounting major students had a mean score of 90.5 with a standard deviation of 10.3. Is there a significant difference between the two sample means? Use 0.01 level of significance.(use t-test)
---------
Ho: mu(econ) = mu(account)
Ha: mu(econ) not equal to mu(account)
z(85.85-90.5)=z(-4.65)=(-4.65-0)/2.4307 = -1.913
p value = 0.0557
But alpha = 1%
Conclusion: Reject Ho. because p value < alpha.
The mean values are not the same.
===================
3 In the contest of Search for Most Outstanding Teacher, 3 candidates are teaching Mathematics, 2 are teaching English, 2 are teaching Science and 1 teaching Filipino. What is the probability that the winner is teaching:
a.P(Mathematics)=3/8
b.P(Science)=2/8
c.P(Filipino)=1/8
d.P(Any subject except English)= 1-(2/8)=6/8
e.P(Any subject except Math)= 1-3/8 = 5/8
4) If the probabilities are 0.40, 0.55 and 0.3 that student will get a failing grade either in Accountancy or Marketing, or in both, what is the probability that he fail at least one of these subjects?
P(fail at least one)= 1-P(fail none)
=1-[P(fail account)+P(fail marketing)-P(fail both)]
=1-[0.40+0.55-0.30]
=1-[0.65]
=0.35
==========
Cheers,
Stan H.

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