Question

Way back in the olden days, Blockbuster tallied all their US movie rental data and found that on average, individuals rent 10 movies a year with a standard deviation of 3. Treat these as population statistics. They wanted to see if movie rental rates in Yuma, Arizona, were different from those of the country as a whole (why Yuma? Who knows ). A random sample of 25 blockbuster members in Yuma yielded a mean rental rate of 11.3 movies per year. Use alpha = .05

Answer 1

Answer with explanation:

By considering the given information we have ,

$H_0: \mu = 10\\\\ H_a: \mu\neq10$

Since, the alternative hypothesis is two tailed so the test is a two-tailed test.

Given : Population mean : $\mu=10$

Standard deviation: $\sigma= 3$

Sample size : n=25 , whihc is less than 30 so the sample is small and we use t-test.

Sample mean : $\overline{x}=11.3$

Significance level : $\alpha= 0.5$

Formula to find t-test statistic is given by :-

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

i.e. $t=\dfrac{11.3-10}{\dfrac{3}{\sqrt{25}}}\approx2.17$

By using the standard normal distribution table,

The p-value corresponds 2.17 (two-tailed)=0.0300068

Since , the p-value is less than the significance level, so we reject the null hypothesis.

Hence, we conclude that there are enough evidence to to support the claim that movie rental rates in Yuma, Arizona, were different from those of the country as a whole .