Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 15 \ months[/tex]
The sample size is n = 25
The sample mean is [tex]\= x = 17 \ months[/tex]
The standard deviation is [tex]s = 5.5 \ months[/tex]
Let assume the level of significance of this test is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 15[/tex]
The alternative hypothesis is [tex]H_a : \mu > 17[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n -1[/tex]
=> [tex]df = 25 -1[/tex]
=> [tex]df = 24[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x- \mu }{\frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 17 - 15 }{\frac{5.5}{\sqrt{25} } }[/tex]
=> [tex]t = 1.8182[/tex]
Generally from the student t distribution table the probability of obtaining [tex]t = 1.8182[/tex] to the right of the curve at a degree of freedom of [tex]df = 24[/tex] is
[tex]p-value = P(t > 0.18182 ) = 0.4286[/tex]
From the value obtained we see that [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.
