Question

In: Statistics and Probability

A university would like to estimate the proportion of fans who purchase concessions at the first...

A university would like to estimate the proportion of fans who purchase concessions at the first basketball game of the season. The basketball facility has a capacity of 3,500 and is routinely sold out. It was discovered that a total of 230 fans out of a random sample of 500 purchased concessions during the game. Construct a​ 95% confidence interval to estimate the proportion of fans who purchased concessions during the game.

The​ 95% confidence interval to estimate the proportion of fans who purchased concessions during the game (____,___)

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample proportion = = x / n = 230 / 500 = 0.46

Z/2 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.46 * 0.54) / 500)

= 0.044

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.46 - 0.044 < p < 0.46 + 0.044

0.416 < p < 0.504

(0.416 , 0.504)


Related Solutions

A university would like to estimate the proportion of fans who purchase concessions at the first...
A university would like to estimate the proportion of fans who purchase concessions at the first basketball game of the season. The basketball facility has a capacity of 3500 and is routinely sold out. It was discovered that a total of 300 fans out of a random sample of 500 purchased concessions during the game. Construct a​ 95% confidence interval to estimate the proportion of fans who purchased concessions during the game. The​ 95% confidence interval to estimate the proportion...
A university would like to estimate the proportion of fans who purchase concessions at the first...
A university would like to estimate the proportion of fans who purchase concessions at the first basketball game of the season. The basketball facility has a capacity of 3,500 and is routinely sold out. It was discovered that a total of 200 fans out of a random sample of 400 purchased concessions during the game. Construct a​ 95% confidence interval to estimate the proportion of fans who purchased concessions during the game. The​ 95% confidence interval to estimate the proportion...
A university would like to estimate the proportion of fans who purchase concessions at the first...
A university would like to estimate the proportion of fans who purchase concessions at the first basketball game of the season. The basketball facility has a capacity of 3 comma 600 and is routinely sold out. It was discovered that a total of 200 fans out of a random sample of 500 purchased concessions during the game. Construct a​ 95% confidence interval to estimate the proportion of fans who purchased concessions during the game. The​ 95% confidence interval to estimate...
The university would like to conduct a study to estimate the true proportion of all university...
The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans. (a) Construct a 95% confidence interval for estimating the true proportion of all university students who have student loans (b) Provide an interpretation of the confidence interval in part (a). (1mark) (c) Conduct an appropriate hypothesis test, at the 5% level of significance...
The university would like to conduct a study to estimate the true proportion of all university...
The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans. (a) Construct a 99% confidence interval for estimating the true proportion of all university students who have student loans (2 marks) (b) Provide an interpretation of the confidence interval in part (a). (1mark) (c) Conduct an appropriate hypothesis test, at the 1% level...
The university would like to conduct a study to estimate the true proportion of all university...
The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans. (a) Construct a 95% confidence interval for estimating the true proportion of all university students who have student loans (b) Provide an interpretation of the confidence interval in part (a). (1mark) (c) Conduct an appropriate hypothesis test, at the 5% level of significance...
The university would like to conduct a study to estimate the true proportion of all university...
The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans. (a) Construct a 99% confidence interval for estimating the true proportion of all university students who have student loans (b) Provide an interpretation of the confidence interval in part (a). (1mark) (c) Conduct an appropriate hypothesis test, at the 1% level of significance...
the university would like to conduct a study to estimate the true proportion of all university...
the university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans. (a) Construct a 95% confidence interval for estimating the true proportion of all university students who have student loans (b) Provide an interpretation of the confidence interval in part (a). (c) Conduct an appropriate hypothesis test, at the 5% level of significance to...
The university would like to conduct a study to estimate the true proportion of all university...
The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans. (a) Construct a 95% confidence interval for estimating the true proportion of all university students who have student loans (2 marks) (b) Provide an interpretation of the confidence interval in part (a). (1mark) (c) Conduct an appropriate hypothesis test, at the 5% level...
The university would like to conduct a study to estimate the true proportion of all university...
The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 217 university students, 88 have student loans. (a) Construct a 99% confidence interval for estimating the true proportion of all university students who have student loans (b) Provide an interpretation of the confidence interval in part (a). (c) Conduct an appropriate hypothesis test, at the 1% level of significance to...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT