**PLEASE NOTE** - I am using Excel and it is CRUCIAL that I know the excel funct
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**PLEASE NOTE** - I am using Excel and it is CRUCIAL that I know the excel functions to discover the answers. PLEASE HELP ME UNDERSTAND THIS BY LISTING THEM!!! Finding the answer isn't as hard for me as being able to input the functions via excel. THANK YOU SO MUCH!!!!
**PLEASE NOTE** - I am using Excel and it is CRUCIAL that I know the excel functions to discover the answers. PLEASE HELP ME UNDERSTAND THIS BY LISTING THEM!!! Finding the answer isn't as hard for me as being able to input the functions via excel. THANK YOU SO MUCH!!!!
Individuals filing federal income tax returns prior to March 31 received an average refund of $1056. Consider the population of wlast-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 Ho will support the researcher's contention b) For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience a population standard devi-ation of a $1600 may be assumed. What is the p-value? c) Did you use the z-distribution or the t-distribution Tell me why. d) At a 05, what is your conclusion? Don't just te me reject or fail to reject". Give an answer appropriate to the context of the question e) Repeat the preceding hypothesis test using the critical value approach Be sure to show all work and label your answers appropriately.Explanation / Answer
a. Ho: Those who file in the last five days have the same average return as those who file earlier.
H1: Those who file in the last five days have a lower average return than those who file earlier.
b. Sample mean is normally distributed random variable. Mean is the population mean and its standard deviation, called the Standard Error (SE) which is equal to the standard deviation divided by the square root of the sample size.
Hence, S.E.= S.D./sqrt(sample size)=1600/sqrt(400)=1600/20=80
So for our observed value of Z we have
Z = (910-1056)/(1600/20) = -146/80 = -1.825
In excel, you can use formula to calculate z-score as,
Z-score=STANDARDIZE(x,Mean,S.E.)
Z-Score=STANDARDIZE(910, 1056, 80)= -1.825
then to calculate P-value=NORM.S.DIST(-1.825,TRUE)= 0.034
c. We have used normal distribution as sample size is greater than 30.
d. At alpha=0.05 and P=0.034
Here, P<alpha, Hence, we do not accept H0 i.e. late filers have a lower average return than those who file earlier.
e. Since our hypothesis isone-sided, (due to lower average return), the rejection region of .05 is in the lower tail, the critical value for Z is -1.645. (from z-table).
Since the Z-calculated is -1.825, is beyond the critical value, in the rejection region, Hence, we do not accept H0.
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