Download Hypothesis Testing

Hypothesis Testing
Individual Quiz
1. The MacBurger restaurant chain claims that the mean waiting time of customers for
service is normally distributed, with a mean of three minutes and a standard deviation of
one minute. The quality assurance department found in a sample of 50 customers at the
Warren Road MacBurger that the mean waiting time was 2.75 minutes. At the 0.05
significance level, can we conclude that the mean waiting time is less than three minutes?
Hint: One population test for large samples
Test statistic:
H0: mean ≥ 3
Ha: mean < 3
The z critical value is -1.6449. We reject for test statistics below that.
Test stat:
z = (2.75-3)/(1/sqrt(50))
z = -1.7678
The test statistic is below the critical value.
We reject the null hypothesis.
The mean waiting time is less than three minutes.
2. Last year a survey in the Nashville TV viewing area showed that 20 percent of the viewers
watched their news on WBEN, which is channel 13. In an effort to increase their rating,
WBEN added several new reporters to cover local stories and events more thoroughly. A
survey last week revealed that out of 400 viewers contacted, 94 watched the news on
WBEN. Can we conclude that the percent of viewers has increased? Use the 0.05
significance level.
Hint: One population proportion test.
Test statistic:
H0: p ≤ 0.2
Ha: p > 0.2
The critical value is z = 1.6449. We reject for test statistics above that.
Test stat:
z = (94/400-0.2)/sqrt(0.2*0.8/400)
z = 1.75
The test statistic is above the critical value.
We reject the null hypothesis.
The new proportion is higher than 20%.
3. A financial planner wants to compare the yield of income and growth oriented mutual
funds. Fifty thousand dollars is invested in each of a sample of 35 income-oriented and 40
growth-oriented funds. The mean increase for a two year period for the income funds is
$1,100 with a standard deviation of $45. For the growth-oriented funds the mean increase
is $1,090 with a standard deviation of $55. At the 0.01 significance level is there a
difference in the mean yield of the two funds?
Hint: Test of two population means based upon two large samples.
Test statistic:
H0: mean1 = mean2
Ha: mean1 ≠ mean2
The critical z values are -2.5758 and 2.5758. We’ll reject the null hypothesis if the test statistic
is outside that range.
Test stat:
z = (1100-1090)/sqrt(45^2/35 + 55^2/40)
z = 0.8655
The test statistic is not outside the critical values.
We do not reject the null hypothesis.
There is no difference in the means between the funds.
4. The average salary of a sample of 14 teachers in a school building with a Master Degree is
$32,741 with a standard deviation of $5,800. A sample of 12 teachers in the same
building without Master Degrees have an average salary of $27,839 with a standard
deviation of $7,400. At the 0.01 significance level, do teachers with Master Degrees have
higher salaries?
Hint: Independent t test for two small samples assuming equal population variance.
Test statistic:
H0: mean1 ≤ mean2
Ha: mean1 > mean2
df = n1+n2-2 = 14+12-2 = 24
The critical T value is: 2.492
We’ll reject the null hypothesis for test stats above that.
Pooled variance:
= ((14-1)*5800^2 + (12-1)*7400^2)/(14+12-2)
= 43320000
Test stat:
= (32741-27839)/sqrt(43320000*(1/14+1/12))
= 1.8932
The test stat is not higher than the critical value.
We do not reject the null hypothesis.
The Masters teachers do not have higher salaries.
5. The President and CEO of Cliff Hanger International Airlines is concerned about high
cholesterol levels of the pilots. In an attempt to improve the situation a sample of seven
pilots is selected to take part in a special program, in which each pilot is given a special
diet by the company physician. After six months each pilot’s cholesterol level is checked
again. At the 0.01 significance level, can we conclude that the program was effective in
reducing cholesterol levels?
Pilot
1
2
3
4
5
6
7
Before
255
230
290
242
300
250
215
After
210
225
215
215
240
235
190
Hint: Dependent samples, paired t test.
Test statistic:
See EXCEL file