## Related questions with answers

A study claims that all adults spend an average of 14 hours or more on chores during a weekend. A researcher wanted to check if this claim is true. This researcher's random sample of 200 adults revealed that these adults put in an average of $14.65$ per hour on housework over the course of a weekend. The $3.00$ hour population standard deviation is well known. a. The alternative hypothesis is that all adults spend more than 14 hours on housework on the weekends. Calculate the $p$-value for the hypothesis test with this alternative hypothesis. At $\alpha=.01$, will you reject the null hypothesis? b. Test the hypothesis of part a using the critical-value approach and $\alpha=.01$.

Solution

VerifiedIn this problem we consider the sample of size $n=200$, with sample mean $\bar{x}=14.65$ and population standard deviation $\sigma=3$.Also, we have level of significance $\alpha=0.01$.

As we see the population standard deviation $\sigma$ is known and the sample size is greater than $30$. So, we can conclude that the given population is normally distributed and we use a normal distribution table to find the observed value of $z$.

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