Question

Super Bowl LIV was played on February 2, 2020 at the Hard Rock Stadium in Miami Gardens, Florida. The Kansas City Chiefs defeated the San Francisco 49ers 31- 20 for their first Super Bowl victory in 50 years. Many people made bets on who would win the Super Bowl, and of interest is to compare the proportion of Kansas City Chiefs fans who placed a bet on the game to the proportion of San Francisco 49ers fans who placed a bet on the game. A random sample of 672 Kansas City Chiefs fans were selected, and 108 said that they placed a bet on the Super Bowl. An independent random sample of 891 San Francisco 49ers fans was selected, and 133 responded that they had placed a bet on the Super Bowl.

(2 points) Is there convincing evidence that the proportion of Kansas City Chiefs fans who placed a bet on the Super Bowl is different from the proportion of San Francisco 49ers fans who placed a bet on the Super Bowl? Use ?? = 0.10. Please do this test byhand using the Classical (Critical Value) Approach.

(2 points) Estimate the difference between the proportion of Kansas City Chiefs fans who placed a bet on the Super Bowl and the proportion of San Francisco 49ers fans who placed a bet on the Super Bowl using a 90% confidence interval. Does your interval support the conclusion you made in part (a)?

(2 points) Do the test in part a again, this time using the SPSS software. Include the appropriate software output, and show the 6-steps of the testing process again (even though you’ve done them in part a). Use the p-value approach with the software.

Answer 1

Is there convincing evidence that the proportion of Kansas City Chiefs fans who placed a bet on the Super Bowl is different from the proportion of San Francisco 49ers fans who placed a bet on the Super Bowl? Use ?? = 0.10. Please do this test byhand using the Classical (Critical Value) Approach.

p1	p2	pc
0.1607	0.1493	0.1542	p (as decimal)
108/672	133/891	241/1563	p (as fraction)
108.	133.	241.	X
672	891	1563	n
	0.0114	difference
	0.	hypothesized difference
	0.0185	std. error
	0.62	z
	.5351	p-value (two-tailed)

Since 0.62 < 1.645, we cannot reject the null hypothesis.

Therefore, we cannot conclude that the proportion of Kansas City Chiefs fans who placed a bet on the Super Bowl is different from the proportion of San Francisco 49ers fans who placed a bet on the Super Bowl.

Estimate the difference between the proportion of Kansas City Chiefs fans who placed a bet on the Super Bowl and the proportion of San Francisco 49ers fans who placed a bet on the Super Bowl using a 90% confidence interval. Does your interval support the conclusion you made in part (a)?

-0.019	confidence interval 90.% lower
0.0419	confidence interval 90.% upper
0.0305	margin of error

The 90% confidence interval for the difference between the proportion of Kansas City Chiefs fans who placed a bet on the Super Bowl and the proportion of San Francisco 49ers fans who placed a bet on the Super Bowl is between -0.019 and 0.0419.

Since the confidence interval contains 0, we cannot conclude that the proportion of Kansas City Chiefs fans who placed a bet on the Super Bowl is different from the proportion of San Francisco 49ers fans who placed a bet on the Super Bowl.

Do the test in part a again, this time using the SPSS software. Include the appropriate software output, and show the 6-steps of the testing process again (even though you’ve done them in part a). Use the p-value approach with the software.

The output is:

Since the p-value (0.5351) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the proportion of Kansas City Chiefs fans who placed a bet on the Super Bowl is different from the proportion of San Francisco 49ers fans who placed a bet on the Super Bowl.