1. An article about women in business claims that 28% of all small businesses in the United States are owned by women. Sally Parks believes that this figure is overstated. A random sample of 2,000 small businesses is selected with 546 being owned by women. Does the sample data provide evidence to conclude that less than 28% of small businesses in the United States are owned by women (with α = .10)? Use the hypothesis testing procedure outlined below.
a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide evidence to conclude that less than 28% of small businesses in the United States are owned by women (with α = .10)
2. The U.S. Bureau of Labor Statistics states that workers in the private sector earn a mean on $10.33 an hour for their first job. A labor economist selects a random sample of 400 private sector workers. This resulted in the following.
Sample Size = 400
Sample Mean = $10.68
Sample Standard Deviation = $2.70
Does the sample data provide evidence that the mean hourly wage for private sector workers for their first job is greater than $10.33 (using α = .10)? Use the hypothesis testing procedure outlined below.
a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide evidence that the mean hourly wage for private sector workers for their first job is greater than $10.33 (using α = .10).