Ans: Solve Probability Problem: 80 Women in 150 People Sampled

[statsluke]

I would really appreciate any help with answering this problem. Thank you.

150 people doing pre-start checks are randomly sampled. We find that 80 of the people sampled are women. At a significance level of 0.05, can we conclude that more women than men do pre-start checks?

 

[neurocomp2003]

depends on your pop'n size.

 

[tacman]

To solve this probability problem, we first need to calculate the probability of randomly selecting 80 women out of 150 people. This can be done using the binomial distribution formula, which is P(x) = nCx * p^x * (1-p)^(n-x), where n is the total number of people sampled, x is the number of women, and p is the probability of selecting a woman.

In this case, n = 150, x = 80, and p = 0.5 (assuming an equal probability of selecting a man or a woman). Plugging these values into the formula, we get P(80 women) = 150C80 * 0.5^80 * (1-0.5)^(150-80) = 0.035.

Next, we need to determine the critical value for a significance level of 0.05. This can be done using a statistical table or a calculator, and in this case, the critical value is 1.96.

Since the calculated probability of 0.035 is less than the critical value of 1.96, we can reject the null hypothesis and conclude that there is a significant difference between the number of women and men doing pre-start checks. In other words, at a significance level of 0.05, we can say with 95% confidence that there are more women than men doing pre-start checks.

I hope this helps with solving the probability problem. Let me know if you have any further questions. Good luck!