Answer: No, the data does not support the claim at 1% level as the mean time is no longer than 4.5 years.
Step-by-step explanation:
Since we have given that
n the California state university system take 4.5 years, on average, to finish their undergraduate degrees.
So, the hypothesis would be
[tex]H_0:\mu=4.5\\\\H_a:\mu>4.5[/tex]
Mean = 5.1
Standard deviation = 1.2
n = 49
So, test statistic value would be
[tex]z=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\z=\dfrac{4.5-5.1}{\dfrac{1.2}{\sqrt{49}}}\\\\z=\dfrac{-0.6}{0.17}\\\\z=-3.53[/tex]
At 1% level of significance, critical value is 2.58
Since 2.58>-3.53.
So, we will accept the null hypothesis.
Hence, No, the data does not support the claim at 1% level as the mean time is no longer than 4.5 years.
