Astudy of 138 penalty shots in world cup finals games between 1982 and 1994 found that the goalkeeper correctly guessed the direction of the kick only 41% of the time. the article notes that this is "slightly worse than random chance." we use these data as a sample of all world cup penalty shots ever. test at a 5% significance 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 of a single proportion p.

b. write the value of the sample statistic, using correct notation. use the sample statistic and the standard error provided to calculate a z-statistic. show your calculation.