Passwords, red heads, and a z test: The BBC reported that red-haired women were more likely...

Passwords, red heads, and a z test: The BBC reported that red-haired women were more likely than others to choose strong passwords (Ward, 2013). How might a researcher study this? Computer scientist Cynthia Kuo and her colleagues conducted a study in which they gave passwords a score, with higher scores going to passwords that are not in “password crack dictionaries” that are used by hackers, that are longer, and that use a mix of letters, numbers, and symbols (2006). They found a mean score of 15.7 with a standard deviation of 7.3. For the purposes of this exercise, treat these numbers as the population parameters. Based on your knowledge of the z test, explain how you might design a study to test the hypothesis that red-haired women create stronger passwords than others.

Expert Solution

For the given scenario, we have to use one sample z test for the population mean. For the given research study, the null and alternative hypotheses are given as below:

Null hypothesis: H₀: Red-haired women do not create stronger passwords than others.

Alternative hypothesis: H_a: Red-haired women create stronger passwords than others.

H₀: µ = 15.7 versus H_a: µ > 15.7

This is a one tailed test (Upper tailed/right tailed).

We will assume level of significance = α = 0.05.

Then we need to collect the sample data for the scores for passwords for red-haired women. After collection of data, we will find the sample mean Xbar. We will collect the adequate sample data (n>30) for using z test or population mean.

Then we will find the test statistic value, critical value, and p-value for this test.

Test statistic formula is given as below:

Z = (Xbar - µ) / [σ/sqrt(n)]

Then we will compare the p-value with alpha value. If the p-value is less than the alpha value, then we will reject the null hypothesis, otherwise we do not reject the null hypothesis. At the final step, we will write the conclusion in context with given scenario.

orchestra answered 2 years ago

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