Question

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?

Answer 1

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

$H_0:\mu=4.5\\\\H_a:\mu>4.5$

Mean = 5.1

Standard deviation = 1.2

n = 49

So, test statistic value would be

$z=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\z=\dfrac{4.5-5.1}{\dfrac{1.2}{\sqrt{49}}}\\\\z=\dfrac{-0.6}{0.17}\\\\z=-3.53$

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.