Question

In: Statistics and Probability

1. Tax returns filed before March 31 get a refund that On average it is $...

1. Tax returns filed before March 31 get a refund that

On average it is $ 1056. Consider the population of "last minute" respondents who present

your statement the last five days of the period for this procedure (normally from April 10 to 15).

An investigator suggests that the reason why these declarants wait until the last

days are due to the fact that on average they get a refund greater than those that they declare before

March 31. In a sample of 400 people who submitted their statement between April 10 and 15,

The average refund was $ 910. From experience it is known that it is possible to consider that

The population standard deviation is e = $ 1600. Use a = 0.10

to. Give appropriate hypotheses so that HO rejection favors the suggestion

of this researcher.

b. Test the above hypothesis using the critical value method. What is your conclusion?

and. Using the method of I p-value. Try the previous hypothesis. What is your conclusion?

d. Create a 99% confidence interval for the population average.

and. Determine the type II (B) and power (1- B) error value for the previous hypothesis test

Solutions

Expert Solution

The Null and Alternative Hypotheses are,

Since the population standard deviation is known, the z test for one population mean is used to test the hypothesis.

Test statistic

The z statistic is obtained using the formula,

Critical value Method

The critical value for the z distribution is obtained from the standard normal distribution table for significance level = 0.10.

Conclusion

Since obtained z statistic = -1.825 is less than the z critical value = 1.28 at a 10% significance level, the null hypothesis is not rejected

P-value Method

The p-value for the z statistic is obtained from the z distribution table z = - 1.825.

Conclusion

Since p-value = 0.966 > 0.10 at a 10% significance level, the null hypothesis is not rejected

and. Determine the type II (B) and power (1- B) error value for the previous hypothesis test

The confidence interval for the mean is obtained using the formula,

The z critical value is obtained from the z distribution table for significance level = 0.01

Type II Error

For the previous hypothesis test, the type II error is obtained using the following formula,

where

(In excel use function =NORM.S.INV(0.90))

From the standard normal distribution table,

(In excel use function =NORM.S.DIST(-0.5434,TRUE)

Power

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,051....

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,051. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). (a) A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support...

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,076....

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,076. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support...

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,081....

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,081. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support...

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,081....

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,064....

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,064. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support...

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,057....

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,057. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). a.A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the...

Individuals filing federal income tax returns prior to March 31 received an average refund of $1077....

Individuals filing federal income tax returns prior to March 31 received an average refund of $1077. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection Ho of will support...

The Internal Revenue Service sampled 20 tax returns and found that the average tax refund was...

The Internal Revenue Service sampled 20 tax returns and found that the average tax refund was $425.39 with a standard deviation of $107.10. Construct a 99% confidence interval for the mean value of all tax refunds. Why do we have a use a t-confidence interval instead of a z-confidence interval for this problem?

The average income tax refund for the 2019 tax year was $3,333. Assume the refund per...

The average income tax refund for the 2019 tax year was $3,333. Assume the refund per person follows the normal probability distribution with a standard deviation of $943. Complete part a) through c) below. a) What is the probability that a randomly selected tax return refund will be more than $2,345? b) What is the probability that a randomly selected tax return refund will be between $1,300 and $2,500? c) What refund amount represents the 40th percentile of tax returns?...

The average income tax refund for the 2009 tax year was $3109. Assume the refund per...

The average income tax refund for the 2009 tax year was $3109. Assume the refund per person follows the normal probability distribution with a standard deviation of $917. Complete parts a through d below. a. What is the probability that a randomly selected tax return refund will be more than $2000? b. What is the probability that a randomly selected tax return refund will be between $1500 and $2900? c. What is the probability that a randomly selected tax return...

Subjects