Answer
a $\bar{x}$ =109 minutes μ=114 minutes,σ=11 minutes,$σ_\bar{s}$ =$ \frac{4.8}{$25}$=1.2, n = 25
α = 0.01/2=0.005, df = 25-1=24, critical value=2.797
t=$ \frac{\bar{x}-μ }{σ_\bar{s}}$
= $ \frac{109-114 }{1.2}$
=-2.27
Rejection region = z< -2.797or z > 2.797
Non rejection region = -2.797 < z < 2.797
The value z = -2.27 falls within the non- rejection region, hence we failed to reject the null hypothesis and conclude that the mean time spent currently by all adults with their families in this city is not different from 114 minutes a day.
b. Yes, we can make a decision for the test of part a without going through the five steps of hypothesis testing. The decision is still the same, of which the null hypothesis is failed to be rejected.
By using p-value approach, it is difficult to get a p-value =0,whereas the sample mean equal to the population mean.
Work Step by Step
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