3. 5.24 Penalty Shots in World Cup Soccer. A study of l 38 penalty shots in World Cup Finals gamcs between 1982 and l994 found that the goalkeeper correctly guessed the direction of the kick only 41% ot'the time. The article notes that this is \"slightly worse than random chance." We use these data as a sample ot'all World Cup penalty shots ever. Test at a 5% signicance level to see whether there is evidence that the percent guessed correctly is less than 50%. The sample size is large enough to use the Normal distribution. The standard error from a randomization distribution under the null hypothesis is SE = 0.043. Let p represent the proportion of all World Cup penalty kicks for which the goalkeeper correctly guesses the direction of the kick. a. State hypotheses in terms ot'a single proportion p. b. Write the value of the sample statistic, using correct notation. c. Use the sample statistic and the standard error provided to calculate a z-statistic. Show your calculation. zstatistic = d. Draw a rough sketch ofa Normal curve below, with z-statistic and appropriate shaded tail region(s). e. Use a Normal distribution in Statkey to nd the pvalue. Include a screen shot of the Normal distribution curve with shaded tail in your homework submission. pvalue = t'. Make a formal statistical decision at the 5% level (Reject Ho i' Fail to reject Ho). g. State the conclusion in context, using nontechnical language