You are a graduate student with interest in bias and stereotypes. You are new at

Question

You are a graduate student with interest in bias and stereotypes. You are new at this, so you begin with terrible research ideas. You initially decide that you are going to waste your career trying to understand how hair color is related to other phenomena. You suspect that there is a bias in reality television regarding the women's hair color. Your first research fiasco on this topic concerns whether blonds appear with more frequency on reality television than they do in the population. You waste a couple hundred hours watching reality television and writing down how many actresses have blond hair and how many have hair of another color. in the United States, the true proportion of natural female blonds is about 209 1. If the probability of being blond (him) is 20%, what is the probability of not being blond Pmot: 1 point for showing work, 1 point for the correct answer)? Polond 0.2 Prot = 2. First, write out the null and alternative hypotheses for this project in symbols (2 points). 3. Now write out both hypotheses in words (2 points). Here are the data from your pointless hours of reality show watching. Complete the table (2 points): 4. Hair Color Blond Not Blond 59 Observed Expected 41 Based on Dechter, E. K. (2015). Physical appearance and earnings, hair color matters. Labour Economics, 32, 15- 26. doi: 10.1016/.labeco.2014.11.002

Explanation / Answer

Solution:-

1)

Pnot = 1 - 0.20

Pnot = 0.80

2)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.20

Alternative hypothesis: P 0.20

3)

Null hypothesis: Probability of being blonde is 20%.

Alternative hypothesis: Probability of being blonde is not 20%.

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.04
z = (p - P) /

z = 5.25

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 5.25 or greater than 5.25.

Thus, the P-value = less than 0.0001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

We can conclude that proportion of blonde is not equal to 20%.

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