Consider the following data drawn independently from normallydistributed populations: (You may find it useful toreference the appropriate table: z tableor t table)

x−1x−1 = 25.7	x⎯⎯2x¯2 = 30.6
σ12 = 98.2	σ22 = 87.4
n1 = 20	n2 = 25

a. Construct the 95% confidence interval for thedifference between the population means. (Negative valuesshould be indicated by a minus sign. Round all intermediatecalculations to at least 4 decimal places and final answers to 2decimal places.)

Confidence internval is _____ to ____.

Consider the following competing hypotheses and accompanyingsample data drawn independently from normally distributedpopulations. (You may find it useful to reference theappropriate table: z table or ttable)

H₀: μ₁ −μ₂ = 0
H_A: μ₁ −μ₂ ≠ 0

x−1x−1 = 51	x−2x−2 = 60
σ1 = 13.00	σ2 = 1.64
n1 = 25	n2 = 25

a-1. Calculate the value of the test statistic.(Negative values should be indicated by a minus sign. Roundall intermediate calculations to at least 4 decimal places andfinal answer to 2 decimal places.)
  

Test statistic:

Researchers at The Wharton School of Business have found thatmen and women shop for different reasons. While women enjoy theshopping experience, men are on a mission to get the job done. Mendo not shop as frequently, but when they do, they make bigpurchases like expensive electronics. The accompanying table showsthe amount spent (in $) over the weekend by 40 men and 60 women ata local mall. The Excel file is also provided. (You mayfind it useful to reference the appropriate table: z tableor t table)

Spending by Men	Spending by Women	Spending by Men	Spending by Women
85	90	87	38
102	79	92	66
139	71	92	100
90	119	72	57
89	90	97	59
52	180	83	89
49	88	118	95
140	56	108	37
90	110	104	86
64	82	110	62
96	64		66
132	129		129
117	28		119
88	13		76
92	140		75
105	62		101
95	32		85
119	220		68
118	72		67
124	90		36
131	80		90
113	56		99
124	82		64
71	56		54
115	88		86
95	104		79
102	54		82
94	108		65
111	86		110
85	88		69

Click here for the Excel Data File

Let µ₁ represent the population mean amountspent by men and µ₂ represent the populationmean amount spent by women.

a. Specify the competing hypotheses that determineif the mean amount spent by men is more than that bywomen.

• H₀: μ₁ −μ₂ = 0; H_A:μ₁ − μ₂ ≠ 0

• H₀: μ₁ −μ₂ ≥ 0; H_A:μ₁ − μ₂ < 0

• H₀: μ₁ −μ₂ ≤ 0; H_A:μ₁ − μ₂ > 0

b. Calculate the value of the test statistic.Assume that the population variances are unknown but equal.(Round intermediate calculations to at least 4 decimalplaces and final answer to 2 decimal places.)

test statistic: