Final answer:
The statement that approximately 1/3 of a sample from a factory where 1/3 of the workforce is female should be female is generally true when using a properly randomized and unbiased sampling method.
Step-by-step explanation:
If we assume that the factory's workforce is representative of the population, and 1/3 of the total number of employees are female, it would be reasonable to expect that approximately 1/3 of a sample taken from this population would also be female. This is because a sample that is properly randomized and unbiased should reflect the same proportions as the total population.
For instance, if the sampling method is truly random, each individual in the population will have an equal chance of being included in the sample irrespective of their gender. Over multiple random samples, one would expect to see the proportion of females in the samples to be close to the proportion of females in the population, which is 1/3. Thus, the statement is generally true; however, individual samples could vary due to sampling variation.
In regards to the given Braily platform questions, let's address them briefly:
- In a population of fish where 42 percent are female, to test if the proportion is less, the null hypothesis (H0) would state that the proportion of female fish is 42 percent or more, while the alternative hypothesis (H1) would propose that the proportion is less than 42 percent.
- To illustrate the relationships between factory workers with a second job and those with a spouse who also works, one could draw a Venn diagram with two overlapping circles representing the two categories.
- In the survey about purchasing decisions, if 120 out of 200 households had women making the majority of purchasing decisions, the estimated population proportion is 120/200 or 60 percent.
- The manager drawing a sample of 30 employees from a workforce of 150 without replacement would find that as the sample is drawn, the chance of any remaining employee being selected increases.
- The central limit theorem would not be appropriate for a sample of just four women due to insufficient sample size for the assumption of normality.