QUESTION 10 0.5 points Save Answ The Table below shows data of two random sample

Question

QUESTION 10 0.5 points Save Answ The Table below shows data of two random samples of employee wages taken from two small business firms providing the same service. The issue to be evaluated is whether the average wage in these two firms is the same. Test this hypothesis at a 0.05. Wages in Firm Wages in Observation Firm A (S) B (S) Observation Firm A (S) Firm B (S) 29363 34035 39034 29784 37682 29679 35320 361031 29864 34304 34093 38730 43698 30293 29658 32119 32081 26 22099 30544 g 40069 33578 377s91 30973 44344 33946 35928 32826 3637 28985 21 25704 30786 33870 32 US8841 3d8161 34993 31358 32308 40703 30827 161 32747 32321 28414 31361 17 32830 30939 351 30870 7921 131 26695 31492 36 34860 34301 Test the hypothesis

Explanation / Answer

here,

claim : TO check the wages in firm A (in $) and the wages in firm B (in $) are significantly differ.

The test hypothesis is

Ho : mu1=mu2

V/s

H1 : mu1 not equal to mu2

Here we have also given that

n1= 36

n2= 36

From the given data we calculate the sample mean

Xbar1=sample mean for firm A = 35036.06

Xbar2= sample mean for firm B = 32511.06

S1^2 =sample variance of firm A = 29983142

S2^2= sample variance of firm B = 11430797

Now

Before proceed to t-test here we need to check the population variances are equal or not.

The null and alternative hypothesis are

Ho : sigma1=sigma2

V/s

H1 : sigma1 not equal to sigma2

Test statistic for F-test

Fstat= (Larger sample variance)/ (smaller sample variance)

= 29983142 /11430797

=2.623014

Critical value

Degrees of freedom for numerator = n1-1 =36-1= 35

Degrees of freedom for Denominator= n2-1 =36-1= 35

level of significance =   = 0.05

we get

Fcritical (0.05 , 35 , 35 ) =1.75714 ( From F table)

Decision rule:

here

Fstat > Fcritical

that is here we fail to accept Ho

i.e population variance are unequal.

So, Here we use unpooled variance

for that

T - statistic is

T-stat = ( x1bar- x2bar) / [ sqrt (s^21/ n1 + s^22/n2 ) ]

Where

Now we want to calculate Spooled

Now we find t test statistic

Tstat= (35036.06-32511.06) / sqrt(29983142/36+11430797/36)

=2525 / 1150387

Tstat =2.354178

and

degree of freedom = smaller d.f of (n1-1) and (n2-1)

= 35

Now we want to find

T critical using MS-EXCEL WE find it

command is

= TINV ( 0.05 , DF)

we get

t critical = 2.030108

Decision rule:

t stat > tcritical

here we fail to accept Ho. ( Null hypothesis )

that is the mean wages of the both firms are significantly differ.

Hence, the option none of the above.

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