Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to conclude that the average is a different number for college students
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The population mean is [tex]\mu = 4[/tex]
The sample mean is [tex]\= x = 3.79[/tex]
The standard deviation is [tex]\sigma = 1.2[/tex]
The level of significance is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : \mu = 4[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 4[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x - \mu }{ \frac{ \sigma }{ \sqrt{n}} }[/tex]
=> [tex]z = \frac{ 3.79 - 4 }{ \frac{1.2}{ \sqrt{50}} }[/tex]
=> [tex]z = -1.237[/tex]
From the z table the area under the normal curve to the left corresponding to -1.237 is
[tex]P(Z < -1.237) = 0.10804[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(Z < -1.237) = 2 * 0.10804[/tex]
=> [tex]p-value = 0.21608[/tex]
Generally 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 conclude that the average is a different number for college students
