> Part (g) Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value. p-value μ 1/2(p-value) 1/2(p-value) 1/2(p-value) μ Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write the appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) απ (ii) Decision: O reject the null hypothesis do not reject the null hypothesis (iii) Reason for decision: O Since a < p-value, we do not reject the null hypothesis. ○ Since α > p-value, we do not reject the null hypothesis. Since a > p-value, we reject the null hypothesis. ○ Since a < p-value, we reject the null hypothesis. (iv) Conclusion: ○ There is sufficient evidence to conclude that an individual's sport of choice is dependent on age. ○ There is not sufficient evidence to conclude that an individual's sport of choice is dependent on age. 1/2(p-value) p-value pane A manager of a sports club keeps information concerning the main sport in which members participate and their ages. To test whether there is a relationship between the age of a member and his or her choice of sport, 644 members of the sports club are randomly selected. Conduct a test of independence at the 5% level. Sport racquetball 44 18 25 26-30 31-40 41 and over 56 30 44 tennis 60 77 39 63 swimming 72 61 64 34 Part (a) State the null hypothesis. O An individual's choice of sport is independent of age. O An individual's choice of sport is dependent on age. Part (b) State the alternative hypothesis. O An individual's choice of sport is independent on age. O An individual's choice of sport is dependent of age. □ Part (c) What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.) Part (d) State the distribution to use for the test. ○ t6 13 Part (e) What is the test statistic? (Round your answer to two decimal places.) Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. ○ If Ho is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. If Ho is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value. ○ If Ho is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value. If Ho is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.