Question

A business student claims that, on average, an MBA student is required to prepare more than five cases per week. To examine the claim, a statistics professor asks a random sample of 10 MBA students to report the number of cases they prepare weekly. The results are exhibited here. Can the professor conclude at the 5% significance level that the claim is true, assuming that the number of cases is normally distributed with a standard deviation of 1.5?

{2, 7, 4, 8, 9, 5, 11, 3, 7, 4}

Answer 1

For this problem, it is helpful to determine the null hypothesis and the alternate hypothesis.

Since the student claims that an MBA student prepares an average of more than 5 cases per week, we can specify our null hypothesis H₀ as:

H₀: The population mean, μ is 5 or less cases per week (μ≤5)

 

The alternate hypothesis, H_a can be specified as the claim the student is making:

Ha: The population mean, μ is > 5 cases per week (μ>5)

 

From the above explanation we can write,

H₀:  μ ≤ 5

H₁:  μ > 5

 

Since we are told that the number of cases is normally distributed with a standard deviation σ = 1.5, we can choose to use a One Sample Z-Test for our hypothesis testing.

 

Let the sample size be, n = 10

 

To proceed, we need to know the mean of the cases from our sample,

= (2+7+4+8+9+5+11+3+7+4) / 10

= 6

 

Next, calculate the Z-Test value according to the following formula,

From the formula,

Symbol	Meaning	Value
x̅	Sample mean	6
μ	Assumed population mean	5
σ	Population standard deviation	1.5
n	Sample size	10

Z =  (6-5) / (1.5/√10) 

= 2.108185

≈ 2.11

 

The Z-Test result is approximately 2.11 and the Z-Score of 2.11 is 0.9826. As a result, the right-tail probability,

p = 1 – 0.9826

= 0.0174

 

To conclude, the p-value is 0.0174 at 5% significance level which is less than the significance level (0.9826).

This indicates that we have enough statistical evidence to reject the null hypothesis in favour of the alternate hypothesis.

 

There is enough evidence to support the claim that, on average, a MBA student required is to prepare more than five cases per week because the p-value is less than significance level of 0.05 and the null hypothesis at 5% level of significance is rejected.