Question

A study claims that college students spend an average of 4 hours or less studying per day. A researcher wants to check if this claim is true. A random sample of 121 college students randomly selected and it showed that average of hours studying per day was 3.15 with a standard deviation of 1.2 hours. Using the 10% significance level, can you conclude that the claim college students spend an average of 4 hours or less studying per day is valid?

Answer 1

Answer with explanation:

Let $\mu$ be the population mean.

By observing the given information, we have :-

$H_0:\mu\leq4\\\\H_a:\mu>4$

Since the alternative hypotheses is left tailed so the test is a right-tailed test.

We assume that the time spend by students per day is normally distributed.

Given : Sample size :  n=121 , since n>30 so we use z-test.

Sample mean : $\overline{x}=3.15$

Standard deviation : $\sigma=1.2$

Test statistic for population mean :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$\Rightarrow\ z=\dfrac{3.15-4}{\dfrac{1.2}{\sqrt{121}}}\\\\\Rightarrow\ z=-7.79166666667\approx-7.79$

Critical value (one-tailed) corresponds to the given significance level :-

$z_{\alpha}=z_{0.1}=1.2816$

Since the observed value of z (-7.79) is less than the critical value (1.2816) , so we do not reject the null hypothesis.

Hence, we conclude that we have enough evidence to accept that the college students spend an average of 4 hours or less studying per day.