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

a.

The Null and Alternative Hypotheses are,

b.

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

c.

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

d.

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 2 years ago
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