Question

A recent study in a small city stated that the average age of robbery victims was 63.5 years. A sample of 20 recent victims had a mean of 63.7 years and a standard deviation of 1.9 years. At α =0.01, is the average age higher than originally believed? Make sure to write down the hypotheses, claim, critical value, test statistic, decision and conclusion

Answer 1

Answer: No, the average age is not higher than originally believed.

Step-by-step explanation:

Since we have given that

Sample size = 20

Mean = 63.7 years

Standard deviation = 1.9 years

So, Hypothesis:

$H_0:\mu=63.5\\\\H_a:\mu>63.5$

So, the value of test statistic would be

$z=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{63.7-63.5}{\dfrac{1.9}{\sqrt{20}}}\\\\z=\dfrac{0.2}{0.425}\\\\z=0.471$

At α = 0.01 level of significance,

critical value z = 2.58

Since 2.58>0.471

so, We will accept the null hypothesis.

Hence, No, the average age is not higher than originally believed.