# Economics Math Problem Week 4 Practice Worksheet (Math Problem Sample)

solving mathematical problems using an assigned case study

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Week 4 Practice Worksheet

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Week 4 Practice Worksheet

Question 1: Can one conclude that there is a difference in the mean times of the Prada and the Oracle at the 0.5 significance point? Elucidate the results to an individual familiar with a single sample test but unfamiliar with the independent mean t- value.

The problem has two values, and they are assigned as follows;

X – The time for Prada in minutes

Y – The time for Oracle in minutes

However, we have to assume that the variables are independent and with uneven variances. Thus, the interest at this juncture is to test the difference in the averages of the two and thus;

X~N (u1, sigma 12) whereas Y ~N (u2, Sigma 22)

(H0) First/ null hypothesis u1 – u2 – 0

(H1) second/ alternative hypothesis: u1 вЂ“ u2 в‰ 0

For a single sample test, there is only one variable that can be assigned the value (S) and an (n) sample size whose variance is unknown. The unknown mean can be presumed to be u0 for H0

The sample mean = S-bar

Sample standard deviation = s

Therefore;

T= (S-bar-u0) sqrt (n)/s that follows a T- distribution under h0 and the df n-1

The above is a single sample test

However, there are two independent samples; X~N (u1, Sigma 12) and Y ~N (u2, Sigma 22). Besides, the sample size is n1 from X and n2 from the value Y. As such, the X-Y ought to follow a standard distribution with the mean u1 – u2 and the variance of Sigma 22 = Sigma 12

Assume that the Y-bar and X-bar are the sample means whereas S2 and S1 are their respective sample standard deviations Following the fact that Sigma 1 and Sigma 2 are unknown they are consequently estimated by S1and S2 respectively. Thus T= {(X-bar- Y-bar)-(u1 – u2)} sqrt(S12/n1 + S22/n2) follow a distribution under H0 u1-u2=0

Therefore, T= {(X-bar- Y-bar) 1/sqrt (S12/n1 + S22/n2) and follows a T-distribution on H0

As such, they are the two independent sample t evaluations from the sample provided that X-bar=12.170, Y-bar=14.875, S1 = 1.056, S2= 2.208, N1 =10 and N2=12. Thus the value of T is 3.76. The alternative hypothesis has two sides and thus rendering the test to be a two- tailed hypothesis

P value = p=2*min {P

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