Question 1105773: For each of the following problems, please provide the requested information.
. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
. (b) Identify the sampling distribution you will us: the standard normal or Student’s t. Explain the rationale for your choice. What is the value of the sample test statistic?
. (c) Find (or estimate) the P − value. Sketch the sampling distribution and show the area corre- sponding to the P − value.
(d) Find the critical value(s).
(e) Based on your answers for parts (a) to (d), will you reject or fail to reject the null hypothesis? Interpret your decision in the context of the application.
36. A Statistics teacher claims that 60% of his students will pass the class with an ”A”. Due to change of text book and educational objectives there is a worry that the number of students getting an ”A” will be smaller now. A random sample of 80 students shows that 43 got an ”A”. Test the teachers claim at significance level of 5%.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! For each of the following problems, please provide the requested information.
. (a) What is the level of significance? 5%
State the null and alternate hypotheses.
Ho: p >= 0.6
Ha: p < 0.6
Will you use a left-tailed, right-tailed, or two-tailed test? left-tailed
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. (b) Identify the sampling distribution you will us: the standard normal or Student’s t. Explain the rationale for your choice. What is the value of the sample test statistic?
Note:: Most texts specify Student's t for tests of proportion.
p(43/80) = (0.5375-0.6)/[0.6*0.4/sqrt(80)] = -1.1411
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. (c) Find (or estimate) the P − value. Sketch the sampling distribution and show the area corresponding to the P − value.
p-value = P(t < -1.1411 when n = 79) = tcdf(-100,-1.1411,79) = 0.12
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(d) Find the critical value(s).
invT(0.05,79) = -1.66; Critical if t < -1.66
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(e) Based on your answers for parts (a) to (d), will you reject or fail to reject the null hypothesis? Interpret your decision in the context of the application.
Since the p-value is greater than 5%, fail to reject Ho.
Since the test statistic does not fall in the critical region fail to reject Ho.
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Problem::
A Statistics teacher claims that 60% of his students will pass the class with an ”A”. Due to change of text book and educational objectives there is a worry that the number of students getting an ”A” will be smaller now. A random sample of 80 students shows that 43 got an ”A”. Test the teachers claim at significance level of 5%.
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Cheers,
Stan H.
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