Penalty Shots in World Cup SoccerA study1 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=0.043.1St.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.

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Asked Nov 18, 2019
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Penalty Shots in World Cup Soccer

A study1 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.


1St.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.

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Expert Answer

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.

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Н.:P20.50 Н.:Р<0.50

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Step 2

The sample proportion, p is 0.41

The sample size is 138.

The test ...

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(P-p) Z= P(1-p) (0.41-0.50) 0.50(1-0.50) 138 -0.09 0.0426 -2.113

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Hypothesis Testing

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