The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts (a) and (b) below. Actress (years) 27 Actor (years) 29 28 61 35 36 31 39 36 33 25 27 41 31 34 47 41 37 35 43 a. Use the sample data with a 0.01 significance level to test the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0 (indicating that the Best Actresses are generally younger than Best Actors). In this example, Hd 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 actor's age. What are the null and alternative hypotheses for the hypothesis test? Ho Hd = 0 year(s) H₁ Hd < 0 year(s) (Type integers or decimals. Do not round.) Identify the test statistic. t= -2.90 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.009 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is less than or equal to the significance level, they won the award than actors. reject the null hypothesis. There is sufficient evidence to support the claim that actresses are generally younger when b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is year(s)

The following are the weights (in pounds) of 14 cows: 96, 99, 128, 151, 157, 179, 219, 249, 255, 301, 324, 345, 387, 390 (a) Find the median of the data. Don’t forget to justify your answer. (b) Draw a reasonable stem-and-leaf display of the data.

Here is a set of sample data. 100 43 19 50 49 37 36 75 46 24 65 18 90 45 21 20 94 74 81 91 35 83 Base on the data above, identify the 5 number summary _,_,_,_,_

How many samples or treatments are here?   490 undergraduate students at a state university in the southwestern region of the United States were surveyed. Each student in the sample was classified according to class standing (freshman, sophomore, junior, or senior) and body are category (body piercings only, tattoos only, both tattoos and body piercings, no body art). Use the data in the accompanying table to determine if there is an association between class standing and body art category. Assume that it is reasonable to regard the sample as representative of the students at this university. Use α = 0.01.                                                             Freshman  Sophmore   Junior    Senior Body Piercings                                          61              7              14          86 Only Tattoos                                             43              11             10         64 Only Mildly Piercings and Tattoos            20                9              7…