A study 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 this data as a sample of all World Cup penalty shots ever to test at a 5% level of significance to see whether there is evidence that the percent guessed correctly is less than 50%. Note that the sample size is considered large enough to use the normal distribution, and the standard error from a randomization distribution under the null hypothesis is SE = 0.043. a. If we let p = the proportion of all World Cup penalty shots guessed correctly, state the Null and Alternative hypotheses.

b. What is the value of the test statistic?

c. What is the corresponding z-score for the test statistic?

d. Find the p-value by looking at the appropriate area in the standard normal distribution.

e. Testing at a 5% level of significance, what is our conclusion. State this in context of this problem.