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Asked Nov 18, 2019

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*Penalty Shots in World Cup Soccer*

A study^{1} 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.^{1}St.John, A., ‘‘Physics of a World Cup Penalty-Kick Shootout - 2010 World Cup Penalty Kicks,” *Popular Mechanics*, June 14, 2010.

What is the *p*-value?

Round your answer to three decimal places.

Step 1

It is given that the population proportion; *P* is 0.50. In the world cup finals, it is found that 41% of time the goalkeeper correctly guessed the direction of the kick. Let *p* be the sample proportion.

The null and alternative hypotheses are given below.

Step 2

The sample proportion, *p* is 0.41

The sample size is 138.

The test ...

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