Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean

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 number of students with part-time or fulltime jobs. A random sample of 81 students shows that 39 have jobs. Do the data indicate that more than 35% of the students have jobs? (Use a 5% level of significance.)
Are we testing a single mean or a single proportion? Assume underlying population distributions are mound-shaped and symmetrical for problems with small samples that involve testing a mean.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling will you use? What assumptions are you making? What is the value of the sample test statistic?
(c) Find (or estimate) the P-value. Sketch the sampling and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.
Distribution
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