Respuesta :
Answer:
Meth Barie's ice cream shop should not introduce the new ice cream flavor.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 4.01
Sample mean, [tex]\bar{x}[/tex] = 4.4
Sample size, n = 15
Alpha, α = 0.1
Sample standard deviation, s = 1.6 minutes
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu \leq 4.01\\H_A: \mu > 4.01[/tex]
We use one-tailed t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{4.4 - 4.0}{\frac{1.6}{\sqrt{15}} } = 0.968[/tex]
Option B) 0.968
Rejection region:
Now, [tex]t_{critical} \text{ at 0.10 level of significance, 9 degree of freedom } = 1.345[/tex]
So the rejection region would be a value of t-statistic greater than 1.345.
Option B) t > 1.345
Conclusion:
Since,
[tex]t_{stat} < t_{critical}[/tex]
We fail to reject the null hypothesis and accept the null hypothesis. Meth Barie's ice cream shop should not introduce the new ice cream flavor.
