Question

Conestoga college recently released a flyer in an attempt to recruit accounting students for their business school. In the flyer, Conestoga college claims that the mean first year graduate salary of their accounting students is $50,000, whereas their biggest competition for accounting students, Fanshawe College, have a first year graduate salary of only $45,000.

After reading Conestoga's recruiting flyer, Fanshawe College executives believe that Conestoga falsely stated the graduate salaries and as a result have conducted their own study. Based on the sample below, at 1% level of significance is there evidence that Conestoga's first year accounting graduates salaries are less than claimed?

Conestoga College First Year Accounting Graduate Salaries
$37,500	$59,250	$36,250	$62,250	$47,000	$59,750	$36,500	$42,500	$38,250	$53,500
$51,500	$49,750	$42,500	$47,000	$39,500	$39,500	$59,750	$38,750	$38,500	$49,250
$42,500	$50,000	$43,500	$59,750	$54,000	$36,000	$52,500	$40,500	$46,750	$57,500
$58,000	$49,500	$41,500	$48,750	$56,750	$54,500	$49,500	$35,500	$55,500	$52,000
$54,000	$37,750	$42,500	$36,250	$52,000	$60,000	$45,250	$58,500	$46,750	$48,250
$52,750	$44,000	$54,250	$43,750	$39,500	$44,250	$55,500	$60,500	$59,250	$50,000
$35,750	$38,500	$44,750	$46,750	$48,250	$62,750	$42,750	$57,500	$62,250	$55,250
$40,750	$56,000	$59,000	$48,750	$52,750	$44,250	$48,750	$36,000	$57,000	$56,750
$39,750	$47,000	$52,250	$40,000	$37,500	$45,000	$35,250	$35,500	$35,250	$41,250
$43,750	$43,500	$56,750	$42,500	$38,000	$62,250	$60,500	$42,250	$56,000	$50,250
$49,000	$54,000	$35,250	$53,750	$60,750	$59,500	$38,000	$42,000	$35,000	$46,250
$38,000	$41,750	$42,000	$48,500	$59,000	$61,500	$42,000	$59,000	$61,750	$53,000
$46,500	$42,000	$62,250	$42,000	$62,750	$43,250	$52,250	$61,750	$39,000	$62,250
$62,750	$56,750	$43,500	$37,500	$43,250	$59,000	$37,000	$41,250	$48,500	$52,000
$36,500	$42,000	$40,250	$52,000	$45,500	$60,750	$46,500	$42,500	$60,750	$46,500
$41,250	$39,500	$51,000	$45,000	$46,750	$61,000	$40,500	$43,000	$53,500	$42,750
$44,500	$53,500	$54,250	$54,250	$39,000	$37,250	$40,750	$48,250	$61,250	$56,500
$46,500	$41,500	$43,250	$59,750	$61,500	$40,000	$53,250	$51,000	$59,750	$47,000
$46,250	$51,750	$53,500	$56,000	$58,500	$42,250	$56,250	$41,250	$62,750	$56,000
$35,250	$53,500	$49,250	$53,750	$62,250	$62,250	$59,250	$53,750	$40,000	$36,250
$36,000	$61,500	$54,250	$51,500	$37,000	$37,000	$59,500	$36,250	$37,500	$48,750
$59,750	$36,500	$42,750	$60,750	$48,000	$40,500	$39,750	$58,500	$57,750	$43,000

BLANK #1: Is this a question involving mean or proportion? ***ANSWER "MEAN" OR "PROPORTION" (WITHOUT THE QUOTATION MARKS)***

BLANK #2: Which type of distribution should be used to calculate the probability for this question? ***ANSWER "NORMAL", "T", OR "BINOMIAL" (WITHOUT THE QUOTATION MARKS)***

BLANK #3: Which of the following options are the appropriate hypotheses for this question: ***ANSWER WITH THE CORRECT LETTER, WITHOUT ANY QUOTATION MARKS OR BRACKETS***

A) H₀: μ = $50,000 H₁: μ > $50,000

B) H₀: μ = $50,000 H₁: μ < $50,000

C) H₀: μ = $50,000 H₁: μ ≠ $50,000

D) H₀: p = $50,000 H₁: p > $50,000

E) H₀: p = $50,000 H₁: p < $50,000

F) H₀: p = $50,000 H₁: p ≠ $50,000

BLANK #4: What is the p-value of this sample? ***ANSWER TO 4 DECIMALS, BE SURE TO INCLUDE LEADING ZERO, EXAMPLE "0.1234"...NOT ".1234"***

BLANK#5: Based on this sample, at 1% level of significance is there evidence that Conestoga's first year accounting graduates salaries are less than claimed? ***ANSWER "YES" OR "NO" (WITHOUT THE QUOTATION MARKS)***

Answer 1

Q1

in this question we are talking about mean salary so we will take mean instead of proportions

Q2

We will use t distribution here while taking out probability because standard deviation of the population is not known.

Q3

Option B is correct

H0 is that mean salary is 50000 and alternative is that it is less than 50000 because it claimed that it is 45000

Q4

after importing this data from excel to R we can easily conduct t test for Ho mean = 50000 and get the p values

here is the code and output of t test conducted and p value is 0.00576

Q5

As we can see that p value = 0.00576 < 0.01 = which implies that we have enough evidence to reject Ho

i.e., mean salary is less than 50000

means that H1 is true