Listed below are ages of actresses and actors at the time that they won an award

Question

Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and Best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.01 significance level. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal Actress's age 18 32 2560 32 Actor's age 41 65 51 In this example, d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the actress's age minus the actors age. What are the null and alternative hypotheses for the hypothesis test? ldentify the test statistic. | | (Round to two decimal places as needed.) Identify the P-value P-value = | | (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is difference between the ages of actresses and actors when they win the award than the significance level | the null hypothesis. There | sufficient evidence to support the claim that there is a

Explanation / Answer

Question 1.

(a) H0 : d = 0

Ha : d 0

(b)

Mean of difference dbar = 15 years

Standard deviation of difference in age sd = 18.1 years

standard error of the mean difference = sd / sqrt(n) = 18.1/ sqrt(5) =  8.1 years

Test Statistic

t = (dbar)/ (sd / sqrt(n) ) = 15/ 8.1 = 1.85

P- value = 0.137

Since the P- value is more than the significance level, we don't reject the null hypothesis. THere is not sufficient evidence......

Question 2

(a) H0 : d = 0

Ha : d 0

OPtion C is correct.

(b) Mean of difference dbar = 26 mm Hg

Standard deviation of difference in age sd = 12.75 mm Hg

standard error of the mean difference = sd / sqrt(n) = 12.75/ sqrt(5) =  5.70 years

Test Statistic

t = (dbar)/ (sd / sqrt(n) ) = 26/ 5.70 = 4.56

P- value = 0.01

Since the P- value is less than the significance level, we reject the null hypothesis. THere is a sufficient evidence......

Actress Actor d 18 41 23 32 41 9 25 65 40 60 51 -9 32 44 12 Average 15 Std. Dev. 18.10

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.