1. A company had its sales persons undergo training, hoping to improve their sales.Past sales data indicate that the average sale was P4,000 per transaction on anormally distributed population. After training, sales data, taken from a randomsample of 25 salesmen/salesladies, indicates an average sale of P4,500 with astandard deviation of P150. (a) Write the null hypothesis. (b) Write the alternativehypothesis. (c) Formulate and calculate the test-statistic. Is it a one-tail or two-tailed test? Did the training work at 95% confidence level? (d) Determine theconfidence interval.

The hypothesis can be constructed as: a) Null hypothesis: H0: µ = P4000 b) Alternative hypothesis:…

Answered: 1. A company had its sales persons…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A company had its sales persons undergo training, hoping to improve their sales.Past sales data indicate that the average sale was P4,000 per transaction on anormally distributed population. After training, sales data, taken from a randomsample of 25 salesmen/salesladies, indicates an average sale of P4,500 with astandard deviation of P150. (a) Write the null hypothesis. (b) Write the alternativehypothesis. (c) Formulate and calculate the test-statistic. Is it a one-tail or twotailed test? Did the training work at 95% confidence level? (d) Determine theconfidence interval.
A company sends a random sample of 16 of its sales people to a course designed to increase their motivation and, hence, presumably their effectiveness. In the following year these people generated sales with an average value of $625,000 and a sample standard deviation of $80,000. During the same period, an independently chosen random sample of 10 salespeople who had not attended the course obtained sales with an average value of $608,000 and a sample standard deviation of $73,000. Assume that the two population distributions are normal and have the same variance. Find a 90% confidence interval estimate for the difference between the population mean sales for sales-people who attended the motivational course and for those salespeople who did not attend the course.
A high school is proud of its advanced chemistry class, in which its 16 students scored an average of 89.3 on the statewide exam, with s = 9. Test the same hypothesis at the .01 level (two-tailed), considering your decision with respect to the null hypothesis, what type of error (Type I or Type II) could you be making?
2.1 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.
Conduct the appropriate hypothesis test and compute the p-value. Sunshine Air has determined that their no-show rate for passengers booked on a flight is 6%. The Airline has recently increased the cost of its travel insurance and and suspects the no-show rate for passengers will decrease. A random sample of 380 reservations resulted in 18 no-shows. At the 0.10 significance level, is there strong enough sample evidence to suggest that the no-show rate in less than 6%?
15. A mail-order business prides itself in its ability to fill customers’ orders in 5 calendar days or less on the average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill their orders. Based upon this sample information, he decides whether the desired standard is being met. He will assume that the average number of days to fill customer orders is 5 or less unless the data strongly suggest otherwise. a. Establish the appropriate null and alternative hypotheses. b. On one occasion where a sample of 45 customers was selected, the average number of days was 5.6, with a sample standard deviation of 1.35 days. Can the operations manager conclude that this mail-order business is achieving its goals? Explain. Use a significance level of 0.05 to answer this question.
In the past, the mean running time for a certain type of flashlight battery has been 9.6 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has decreased as a result. A hypothesis test is to be performed. Determine the null and alternative hypotheses. A. H0: µ ¥ 9.6 hours and H1: µ = 9.6 hours B. H0: µ = 9.6 hours and H1: µ ¥ 9.6 hours C. H0: µ = 9.6 hours and H1: µ > 9.6 hours D. H0: µ = 9.6 hours and H1: µ < 9.6 hours
A researcher administers a treatment to a sample from a population with a mean of m=50. If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect, the the null hypothesis states that m=40. True or false?
The National Institute of Mental Health published an article stating that in any two-year period, approximately 10.5percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 150 people in a certain town, eight of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?
Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go") so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that of its customers order their food to go. Suppose that this proportion is correct and that a random sample of individual customers is taken. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of customers in the sample who order their food to go by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.
Is there a significant difference in the unemployment rates among Hispanic and white adults in the state of Texas? Based on data collected by the Texas Workforce Commission, 4.6% of 640 randomly selected Hispanic adults are unemployed while 2.8% of 780 randomly selected white adults are unemployed. Does this data provide statistically significant evidence that there is a difference in the unemployment rates between the two groups? a) State the null hypothesis (H0) and the alternative hypothesis (Ha ) for the significance test and the conditions b) assume the conditions are satisfied, identify the test statistic (z or t?) to be used, and show the formula for the test statistic, and enter the appropriate values in the formula. (don’t calculate the test statistic here.) c) Assume that the standard error of the differences in proportions is SE = 0.00995. Using this SE, calculate the value of the test statistic (which you set up in part (b) and find the p-value d) Using a significance…
1. A study by a bank compared the average savings of customers who were depositors for three years or less with those who had been depositors for more than three years. The results of a sample are: less than equal to 3 years greater than 3 years Mean Savings Balance $1,200 $1,250 Population Standard deviation $100 $150 Sample Size 10 15 To test that the two groups of customers have equal savings rates, what is the p-value for a two-tailed test? 2. A financial planner wants to compare the yield of income and growth mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income and 40 growth funds. The mean increase for a two-year period for the income funds is $900. For the growth funds, the mean increase is $875. Income funds have a sample standard deviation of $35; growth funds have a sample standard deviation of $45. Assume that the population standard deviations are equal. At the 0.05 significance level, is there a difference in the mean yields of…

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