HW 4 Making inferences: BUSN 5000

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1. Make sure the first letter in the answer is NOT capitalized. It will say your answer is wrong even if you're right. EXCEPTION: Acronyms are capitalized 2. for questions with multiple answers make sure you put a comma between the answers plus a space after the comma.

We reject the null hypothesis at the 5% level if the value of the 𝑡t statistic is greater than _____ in absolute value.

1.96

Men are _____ percentage points more likely to work more than 40 hours.

16

Women are _____ percentage points more likely to have a college degree.

2

Men in this group work on average _____ hours and _____ minutes per week more than women.

2, 15

For women in this group, average log wages rise from roughly _____ to _____ (round to the nearest 0.15 log wage), or in dollar terms, roughly $ _____ to $ _____ (round to the nearest dollar).

2.4, 3, 11, 20

Men work on average _____ more hours per week than women. (Report to two decimals.)

2.64

Among the group documented in Table 2, the gender wage gap is roughly _____ %. (Round to the nearest whole number.)

23

The absolute value of the test statistic is _____. (Round to two decimal places.)

3.76

The percentage wage gap is roughly _____ %. (Round to the nearest whole percent.)

34

Looking closely at Figure 1 (or the printout of the data frame), the confidence intervals for the male CEF contain the estimated conditional mean for women in _____ out of 8 years.

4

The absolute value of the 𝑡t statistic for the null that there is no gender gap in log wages among 23-62 year-olds is _____ (round to nearest integer), which implies the null is _____ at the 5% level (or pretty much any other level for that matter).

41, rejected

Women comprise ____ % of our sample of 23-62 year-olds. (Round to the nearest whole number.)

43

Based on Figure 8 in the slide deck, it appears that the confidence intervals for average log wages overlap up to year _____ of a career.

5

Earnings is a measure of both ______ and ______ , which masks productivity.

7

There are _____ individuals in the sample of 23-30 year-olds with college degrees working more than 40 hours and women comprise _____% (round to the nearest whole number) of this group.

868, 43

PART B: BELOW THIS CARD

PART B: BELOW THIS CARD

Consistency means that as the sample size increases, both ______ and ______ approach zero.

bias, sampling error

If an estimator approaches the underlying estimand as sample size grows, we say the esimator has the property of ______ .

consistency

To test whether the gender gap in average log wages is equal to zero, you divide the _____ in average log wages between women and men by the _____ of the difference.

difference, standard error

In principle, any estimate can be decomposed into three parts: 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒=______+______+______

estimand, bias, sampling error

A 𝑡t test compares the _____ you obtain from the sample with the hypothesized value of the estimand divided by the _____ of the estimator.

estimate, standard error

Like before, we start by loading the data. Because the dataset is in an Excel (.xlsx) format we will use the read_xlsx function from the readxl package. Recall that we load packages with the library command and name of the data file is cps09mar.

library(readxl) cps_mar <- read_xlsx("./data/cps09mar.xlsx")

Wages are more variable among _____ and hours are more variable among _____.

males, males

If an estimator obeys the CLT, we can treat its sampling distribution as ______ for large sample sizes.

normal

A confidence interval tells how likely an estimate we calculate is close to its target in the ______ .

population

The reason we want to move from earnings to wages is that the story is really about ______ .

productivity

Our framework for using data to learn about the world is gathering ______ from the ______ of interest to infer features of the data-generating process.

random samples, population

The value of the test statistic suggests that we should _____ (reject/fail to reject) the null hypothesis at the 5% level.

reject

The square root of the estimated variance of an estimator is called the _____ .

standard error

Statistical hypothesis tests translate information contained in a confidence interval into _____ answers to particular questions.

yes/no