Free Printable Statistical Inferences about Two Means

1.

What is the primary goal when comparing two populations in this context?

a)

Determine whether there is a significant difference between the two population means

b)

Compute the median for each population and compare visually

c)

Estimate the variance of a single population

d)

Construct a confidence interval for one population proportion

2.

In the same context of comparing average salaries of marketing and production managers, choose the rearranged form that is equivalent to the null hypothesis.

a)

$\mu_M - \mu_P = 0$

b)

$\mu_M - \mu_P \ne 0$

c)

$\mu_M + \mu_P = 0$

d)

$\mu_P - \mu_M = 1$

3.

Independent samples are selected from the two populations with sample sizes shown. What are the sample sizes for the two groups used in this analysis?

a)

n1 = 50, n2 = 50

b)

n1 = 100, n2 = 100

c)

n1 = 75, n2 = 125

d)

n1 = 120, n2 = 80

4.

Compute the point estimate of the difference in population means using the given sample means. Given $\bar{x}_1 = 34.5$ and $\bar{x}_2 = 42.4$ , what is $\bar{x}_1 - \bar{x}_2$ ?

a)

−7.9

b)

7.9

c)

−77.9

d)

−3.9

5.

Determine the standard error for the difference in sample means using the displayed formula and values. Using $\sigma_{\bar{x}_1-\bar{x}_2} = \sqrt{\frac{11^2}{100} + \frac{16^2}{100}}$ , what is the standard error?

a)

1.4142

b)

1.6449

c)

1.9416

d)

2.5750

6.

Identify the critical value shown for the stated confidence level. For a 95% confidence interval, what z-value is used?

a)

1.28

b)

1.645

c)

1.96

d)

2.575

7.

A major bank wishes to develop a 95% confidence interval estimate for the difference in population means for spending by unmarried versus married card holders, and they do not believe the population standard deviations are equal. Which procedure should be used to construct the interval for $\mu_1-\mu_2$ ?

a)

Two-sample t interval with unequal variances (Welch’s method)

b)

Two-sample pooled t interval assuming equal variances

c)

Two-sample z interval with known population standard deviations

d)

One-sample t interval for a single mean

8.

Based on the calculations shown, what is the 95% confidence interval for $\mu_1-\mu_2$ (unmarried minus married)?

a)

$137.53$ to $234.87$

b)

$118.25$ to $254.15$

c)

$106.90$ to $265.50$

d)

$120.00$ to $240.00$

9.

What is the observed difference in sample means used in the interval calculation for $\bar{x}_1-\bar{x}_2$ ?

a)

$186.20$

b)

$137.53$

c)

$234.87$

d)

$48.67$

10.

According to the sample summary presented, which group has the higher mean spending?

a)

Unmarried customers

b)

Married customers

Statistical Inferences about Two Means — Worksheet Extraction

Total questions: 10

Worksheet time: 5mins

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