Stats Solution

Problem set 1

1. Difference between 2 means = Sample mean salary male – sample mean salary female = 3

1. When the population standard deviation is known and sample size > 30, we use the the Z distribution else we use t distribution. Answer would be a)

3)

Standard deviation = SE = sqrt[ (s12/n1) + (s22/n2) ]

where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Answer would be d)

4) Margin of error = Zα/2 σ = 1.96*2 = 3.92

5) b) is the correct hypothesis

6) We established that we would be using Z distribution.

Z score = point estimate / standard deviation = 3/2 = 1.5

7) Refer the Z table

Get the p value at Z score = 0.9332

Required value = 1- 0.9332 = 0.0668

8) Since p value = 0.0668 > 0.05, we don’t reject the null hypothesis and conclude that the population salaries and males and females are equal

Problem set 2

1. Point estimate = Downtown store sample mean – North mall store sample mean = 9-8 = 1

1. When the population standard deviation is known and sample size > 30, we use the the Z distribution, else we use t distribution. This, we would use t distribution

1. Standard deviation =SE = sqrt[ (s12/n1) + (s22/n2) ]

where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Answer would be c) 0.46

1. a) is the correct hypothesis option

1. T score = point estimate / standard deviation = 1/ 0.46 =2.17

1. Refer the t table. Use degrees of freedom as 37. T critical value = t0.025 = 2.026

1. Since t score > t critical value, we reject the null hypothesis. Thus, the population average wage of downtown store is significantly different from that of north mall store

Problem set 3

1. Point estimate = d= mean of all di = (2 – 4 -2 +0 -1) = -5/5 = -1

1. Standard deviation =

sd = sqrt [ (Σ(di - d)2 / (n - 1) ]

 where di is the difference for pair i, d is the sample mean of the differences, and n is the number of paired values.

Use the formula to get the answer