Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the average room price is significantly different from $108.50
Step-by-step explanation:
From the question we are told that
The sample size is n = 64
The average price is [tex]\= x = \$ 112[/tex]
The population standard deviation is [tex]\sigma = \$ 16[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The population mean is [tex]\mu = \$ 108.5[/tex]
The null hypothesis is [tex]H_o : \mu = 108.50[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 108.50[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{ \sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{112 - 108.50 }{ \frac{ 16}{\sqrt{64} } }[/tex]
=> [tex]z = 1.75[/tex]
From the z table the area under the normal curve to the left corresponding to 1.75 is
[tex]P( Z > 1.75) = 0.040059[/tex]
Generally p-value is mathematically represented as
[tex]p-value = 2 * P( Z > 1.75)[/tex]
=> [tex]p-value = 2 * 0.040059[/tex]
=> [tex]p-value = 0.08012[/tex]
From the values 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 average room price is significantly different from $108.50
