Question

please help with parts b and c

A survey reported the number of meters (m) per week swam by two groups of swimmers—those who competed exclusively in breaststroke and those who competed in the individual medley (which includes breaststroke). The number of meters per week practicing the breaststroke was recorded for each swimmer, and the summary statistics are given below. Is there sufficient evidence to indicate that the average number of meters per week spent practicing breaststroke is greater for exclusive breaststrokers than it is for those swimming individual medley? Specialty Exclusively Breaststroke | Individual Medley Sample size 130 80 Sample mean (m) 9,017 5,653 Sample standard deviation (m) 71,320 19,110 Population mean 42 (a) State the null and alternative hypotheses. (Use y, for exclusively breast stroke swimmers and y, for individual medley swi O Ho: My > M2 Hai My = M2 Ho u = 42 Hai Mp < M2 Ho: 41 = 42 Hill & M2 Ho: 41 * uz H: 4, = uz Ho: 41 = 42 Haily > M2 . (b) What is the appropriate rejection region for an a = 0.01 level test? (Assume the test statistic will be calculated using exclusively breast stroke swimmers - individual medley swimmers. Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) 2 > (c) Calculate the observed value of the appropriate test statistic. (Calculate the test statistic using exclusively breast stroke swimmers – individual medley swimmers. Round your answer to two decimal places.) z =

Answer 1

The statistical software output for this problem is:

Two sample Z summary hypothesis test: Mean of population 1 (Std dev = 71320) H: Mean of population 2 (Std dev = 19110) H-: Difference between two means H:H-42 = 0 HAL-H2> 0 Hypothesis test results: Difference , 12 Sample mean Std. err. Z-stat H-2 130 80 3364 6610.0038 0.50892558 P-value 0.3054

Hence,

b) For 0.01 significance level,

z > 2.33

z < NONE

c) z = 0.51