The operations manager of a motor vehicle accessories firm with branches in Limpopo and Durban wants to establish whether their Limpopo branch is performing better than their Durban branch in terms of the average size of orders received. Both branches have been operating for only one year. A random sample of 31 orders from the Limpopo branch had an average value of R355.20 with a standard deviation equal to R151.50. Orders received by the Durban branch of the firm were also randomly sampled. The average of the 35 orders sampled was R265.60 with a sample standard deviation of R162.20. Can the operations manager conclude, at the 3% significance level, that the Limpopo branch is performing better than the Durban branch? Show the null and alternative hypotheses for the test and draw the appropriate conclusion. Compute the p-value

Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2.   Step 2 of 3 :   Compute the value of the test statistic. Round your answer to two decimal places.

A sample of 76 female workers and another sample of 48 male workers from a state produced mean weekly earnings of $743.50 for the females and $777.63 for the males. Suppose that the population standard deviations of the weekly earnings are $80.05 for the females and $88.68 for the males. The null hypothesis is that the mean weekly earnings are the same for females and males, while the alternative hypothesis is that the mean weekly earnings for females is less than the mean weekly earnings for males. Directions: • Label your answers with the correct statistical symbols. • If you use the Ti, identify which function and values you used to calculate. If you solve by hand, show all steps 2.5 The significance level for the test is 1%. What is/are the critical value(s)? 2.6. What is the value of the test statistic, rounded to three decimal places? 2.7. What is the p-value for this test, rounded to four decimal places? 2. 8. Using the p-value approach, do you reject or fail to reject the null…

Insurance Company A claims that its customers pay less for car insurance, on average, than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 12people who buy insurance from Company A, the mean cost is $153 per month with a standard deviation of $16. For 15 randomly selected customers of Company B, you find that they pay a mean of $160 per month with a standard deviation of $10. Assume that both populations are approximately normal and that the population variances are equal to test Company A’s claim at the 0.10 level of significance. Let customers of Company A be Population 1 and let customers of Company B be Population 2. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. H0: μ1=μ2 Ha: μ1_____μ2 Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places Step 3 of…

According to Kaiser Family Foundation survey in 2011 and 2010, the average premium for employer-sponsored health insurance for family coverage was $15,073 in 2011 and $13,770 in 2010 (USA TODAY, September 29, 2011). Suppose that these averages were based on random samples of 250 and 200 employees who had such employer-sponsored health insurance plans for 2011 and 2010, respectively. Further assume that the population standard deviations for 2011 and 2010 were $2160 and $1990, respectively.

A newly hired basketball coach promised a high- paced attack that will put more points on the board than the team's previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach's claim. He takes a sample of 36 of the team's games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points. Over the past 10 years, the team had averaged 99 points. What is(are) the appropriate critical value(s) to test the new coach's claim at the 1% significance level? -2.438 -2.438 and 2.438 2.326 2.438

Kendra, the Human Resources manager for Moore Manufacturing wants to determine whether the employee retention rate is higher for the company's Eastern Division than it is for the Western Division. A random sample of 25 employees from Moore Manufacturing's Eastern Division (group 1) has an average time with the company of 4.8 years and a standard deviation of 1.1 years. A random sample of 23 employees from Moore Manufacturing's Western Division (group 2) has an average time with the company of 4.1 years and a standard deviation of 0.9 years. Conduct a hypothesis test at 0.02 significance. Round answers to 4 decimal places where appropriate. The Null and Alternative Hypothesis are: Ho: mew1 = mew2 and H1: mew1 > mew2.  The appropriate distribution is Student's t. What is the test statistic? What is the p-value? State the appropriate conclusion based on the information.

A pharmaceutical company needs to know if its new cholesterol drug, Praxor, is effective at lowering cholesterol levels. It believes that people who take Praxor will average a greater decrease in cholesterol level than people taking a placebo. After the experiment is complete, the researchers find that the 34 participants in the treatment group lowered their cholesterol levels by a mean of 22.2 points with a standard deviation of 3.4 points. The 42 participants in the control group lowered their cholesterol levels by a mean of 21.2 points with a standard deviation of 1.8 points. Assume that the population variances are not equal and test the company's claim at the 0.10 level. Let the treatment group be Population 1 and let the control group be Population 2. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Ho:₁ = ₂ Ha: M •M₂

In one city, the average amount of time that tenth-graders spend watching television each week is 23 hours. The principal of Birchwood High School believes it is less for the 10th grade students that at his school.  For a sample of 95 tenth-graders from the school, the mean amount of time spent watching television per week was 21.9 hours.  Assuming a population standard deviation of 3.1 hours, does the data provide sufficient evidence to conclude that for all tenth-graders at Birchwood High school, the mean amount of time spent watching television per week is less than the city average of 23 hours?  Perform the appropriate hypothesis test using a significance level of 0.005.  What are the hypotheses?         What is the test statistic? Is it a z or a t?         Find the P-value for this test statistic. How does it compare to the significance level?  On the normal curve, indicate the location of the test statistic  and  the p-value. (label them on the graph)                 Write…

According to the Bureau of Labor Statistics, the mean salary for registered nurses in Kentucky was $55,130. The distribution of salaries is assumed to be normally distributed with a standard deviation of $5,778. Someone would like to determine if registered nurses in Ohio have a greater average pay. To investigate this claim, a sample of 220 registered nurses is selected from the Ohio Board of Nursing, and each is asked their annual salary. The mean salary for this sample of 220 nurses is found to be $55,504.488.  Completely describe the sampling distribution of the sample mean salary when samples of size 220 are selected. mean:  μ x-bar = ____ standard deviation: σ x-bar  = ____ shape: the distribution of is ____________(not normally distributed/normally distributed) because ___________ (the sample size is large/the sample size is not large/the population of salaries is normally distributed/the population of salaries is not normally distributed)