Question
Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the
Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of81students shows that37have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance.
What are we testing in this problem?
single mean
single proportion
(a) What is the level of significance?
State the null and alternate hypotheses.
H0:p= 0.35;H1:p0.35
H0:p= 0.35;H1:p> 0.35
H0:= 0.35;H1:> 0.35
H0:p= 0.35;H1:p< 0.35
H0:= 0.35;H1:< 0.35
H0:= 0.35;H1:0.35
(b) What sampling distribution will you use? What assumptions are you making?
The Student'st, sincenp< 5 andnq< 5.
The standard normal, sincenp> 5 andnq> 5.
The Student'st, sincenp> 5 andnq> 5.
The standard normal, sincenp< 5 andnq< 5.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find (or estimate) theP-value.
P-value > 0.250
0.125 <P-value < 0.250
0.050 <P-value < 0.125
0.025 <P-value < 0.050
0.005 <P-value < 0.025
P-value < 0.005
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?
At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs.
There is insufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs.
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