Answer:
There is no sufficient evidence to support the claim that mean commuting time is more than 1.9 hours
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 1.9 \ hr[/tex]
The sample mean is [tex]\= x = 2.2[/tex]
The standard deviation is [tex]\sigma = 0.7[/tex]
The sample size is [tex]n = 14[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = 1.9 \ hr[/tex]
The alternative hypothesis is [tex]H_a : \mu > 1.9 \ hr[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]
[tex]t = \frac{ 2.2 - 1.9 }{ \frac{0.7 }{ \sqrt{14} } }[/tex]
[tex]t = 1.6036[/tex]
The p-value is obtained from the z-table, the value is
[tex]p-value = P(t > 1.6036) = 0.054401[/tex]
Looking at the value of [tex]p-value \ and \ \alpha[/tex] we see that [tex]p-value > \alpha[/tex]
So we fail reject the null hypothesis
Hence we can conclude that there is no sufficient evidence to support the claim that mean commuting time is more than 1.9 hours
