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# Tutorial 10

Hypotheses Testing
1. The following information is available
H o : µ = 50
H 1 : µ ≠ 50
The sample mean is 49 and the sample size is 36.The population follows the
normal distribution and the standard deviation is 5.Use the 0.05 significance level.

2. The Mac Burger restaurant chain claims that the waiting time of customer for service
is normally distributed, with a mean of 3 minutes and a standard deviation of 1
minute. The quality-assurance department found in a sample of 50 customers at the
Warren Road Mac Burger that the time waiting was 2.75 minutes. At the 0.05
significance level, can we conclude that the mean waiting time is less than 3
minutes?

## 3. Given the following Hypotheses

H 0 : µ = 400
H 0 : µ ≠ 400
For a random sample of 12 observations, the sample mean was 407 and the sample
standard deviation 6. Using the 0.01 significance level
a) State the decision Rule
b) Compute the value of the test statistic

## 4. Given the following hypothesis

H O : µ = 100
H O : µ ≠ 100
A random sample of six resulted in the following values 118, 105, 112, 119, 105,
and 111. Using the 0.05 significance level, can we conclude the mean is different
from 100?
a. State the decision rule?
b. Compute the value of statistic
c. What is your decision regarding the null Hypotheses?
d. Estimate the p-value?

5. Mary Jo Fitzpatrick is the Vice President for Nursing Services at St. Luke’s
Memorial Hospital. Recently she noticed that unionized job for nurses seem to offer
higher wages. She decided to investigate and gathered the following sample
information.

Sample Standard
Group Mean Wage Deviation Sample size
Union \$20.75 \$2.25 40
Nounion \$19.80 \$1.90 45
Would it be reasonable for her to conclude that union nurses earn more? Use the 0.02
significance level. What is the p-value.
6. Ms Lisa Monnin is the budget director for Nexus Media , Inc. She would like to
compare the daily travel expenses for the sales staff and the audit staff. She collected
the following sample information.

Sales
(\$) 131 135 146 165 136 142
Audit(\$) 130 102 129 143 149 120 139

At the 0.10 significance level, can she conclude that the mean daily expenses are
greater for the sales staff than the audit staff? What is the p-value?

## 7. The null and alternate hypotheses are

H 0 : µd = 0
H1 : µ d ≠ 0

8. The following paired observations show the number of traffic citation given for
speeding by officer Dhont and Officer Meredith of the South Carolina Highway
patrol for the last five months
DAY
May June July August September
Officer Dhont 30 22 25 19 26
Officer
Meredith 26 19 20 15 19
At the 0.05 significance level, is there a difference in the mean number of citation
given by the two officers?
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