A visual memory test shows that when young adults (mean age 24 years) try to memorize 20 line drawings of common objects, they recognize 15 of these, on average, in a surprise test four weeks later. This population of scores is normal with a standard deviation of 2.4. A researcher was interested in whether older adults perform better on the task compared to young adults. Therefore, he chose a random sample of 36 older adults (mean age 71.2 years) and had them do the same task.Note that you can write mu, instead of, as the population mean; and sigma, instead of as the population standard deviation. Answers in four decimal place a. State the null hypothesisin symbols.H₀: b. State the alternative hypothesisin symbols. H₁: c. The older adults correctly recognized a mean of 15.3 items. Calculate z_{obs. First, write your calculation:. Then, write your answer:} d.What p-value is associated with z_obs?Please, write 4 decimal points. p e.If we adopt the p < .05 significance level, is z_obs statistically significant? (yes/no) f.Should you retain or reject H₀? (retain/reject)