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# Hypothesis Testing

### Hypothesis test exercise

A postal researcher wanted to test the theory that a higher response rate is achieved when a postal questionnaire is sent out with a personalized covering letter (A) than when the covering letter is impersonal (B). Two random samples of 100 people were selected. When the questionnaires were dispatched, the first sample-receive

### Predicted Value of Standardized Test Statistics

1. Given the equation of a regression line is y=-2.5x-7.6, what is the best predicted value for y given x=4.1? Assume that the variables x and y have a significant correlation. A. -2.65 B. 17.85 C. -17.85 D. 2.65 2. You wish to test the claim that the mean>23 at a level of significance of alpha=0.05 and are given sample

### Finding Standardized Test Statistics in Samples

1. Suppose you want to test the claim that the mean does not equal 3.5. Given a sample size of n = 31 and a level of significance of when should you reject H0 ? a. Reject H0 if the standardized test statistic is greater than 2.33 or less than -2.33 b. Reject H0 if the standardized test statistic is greater than 1.645 or les

### Working with z distribution

Nicotine in cigarettes. To determine whether the mean nicotine content of a brand of cigarettes is greater than the advertised value of 1.4 milligrams, a health advocacy group tests H0: ¹ = 1:4 Ha: ¹ > 1:4 The calculated value of the test statistic is z = 2:42. (a) Is the result significant at the 5% level? (b) Is the res

### Two or More Sample Hypothesis Testing

Using the data set attached, develop one business research question from which you will formulate a research hypothesis that will test two or more populations. Describe the results of a hypothesis test of two populations or more than two populations (ANOVA). Include the following: i. Formulate both a numerical and verbal h

### Hypothesis Testing: Critical Values and Decision Making Problems

You will be asked to determine the correct decision (Reject Ho or Fail to Reject Ho) for each of the following tests of hypotheses. 1. A hypothesis test at the 0.025 level of significance with a p-value for the sample of 0.0075. 2. A hypothesis test at the 0.01 level of significance with a p-value for the sample of 0.012

### Hypothesis Testing: Population Mean and Proportion

Does Lavastatin reduce the risk of heart attack? In a Texas Study, researchers gave Lovastatin to 2,325 people, and a inactive substitute to 2,081 people, with an average age of 58. After 5 years, 57 of the lovastatin group suffered a heart attack, compared with 97 for the inactive pill. The level of significance of the test

### Statistics - Minimize Z = 1.80S + 2.20T

2) Minimize Z = 1.80S + 2.20T Subject to: 5S + 8T => 200 15S + 6T => 240 4S + 12T => 180 T => 10 S, T => 0 (a) What are the optimum values of the decision variables and Z?

### The solution to Hypothesis testing of Mean: Five step method

1. Determine whether the hypothesis test for each claim is left-tailed, right-tailed, or two tailed. Explain your reasoning. Lung Cancer: A government report claims that the proportion of lung cancer cases that are due to smoking is 87% 2. Testing Claims. (a) write the claim mathematically and identify H0 and Ha. (b)

### Determination of Rejection Region

A coin-operated coffee machine dispenses a preset amount of coffee. The vending company wants to know if the average amount dispensed is µ = 6 (H0, no adjustment needed) or is µ = 6 (Ha, requires adjustment). Which of the following is an appropriate rejection region for conducting the above test at significance level .05 if

### Rising FAX Costs

Chapter Exercises 9.54 Faced with rising FAX costs, a firm issued a guideline that transmissions of 10 or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44

### Sample Size of Purchase Amounts

Purchase Amounts for all Customers Shopping at a Local Supermarket on a Given Friday Customer Amount 1 \$35.97 2 \$52.23 3 \$93.08 4 \$2.90 5 \$91.13 6 \$150.69 4. Problem 4 contains data of the amount that customers spend in a supermarket on a specific Friday. Assume this data represents the pop

### Statistics - Null and Alternate Hypothesis.

7. A fast-food franchiser is considering building a restaurant at a certain location. Based on financial analysis, a site is acceptable only if the number of pedestrians passing the location averages more than 100 per hour. A random sample of 50 hours produced a sample mean of 110 pedestrians per hour. Historical studies ha

### Statistics - Population Means, Known and Unknown

C. Say a fast-food franchiser is considering building a restaurant in a local mall. According to franchise headquarters, a site is acceptable only if the number of pedestrians passing the location averages more than 100 per hour. A random sample of 40 hours produced a sample mean of 105 persons and a sample standard deviation o

### Hypothesis Tests of Equality of means of two populations.

Data Analysis 32. Consider a random sample of 100 households from a middle-class neighborhood that was the recent focus of an economic development study conducted by the local government. Specifically, for each of the 100 households, information was gathered on each of the following variables: family size, location of th

### One Sample Hypothesis Testing

Using ratio or interval numerical data from the data set attached, develop the following: 1. Develop a research question 2. Formulate a research hypothesis and null hypothesis 3. Decide the type of test and level of significance 4. Calculate the standard error 5. Find the critical region 6. Perform the hypothesis te

### State your Null and Alternative hypothesis

Please state your null and alternative hypothesis for the following cases. Please explain how do you make that decision on which is alternative and which is null. Remember that it comes to the point that what a researcher would like to test for. For example, when I test to see if a sereal box weighs as it is stated, I am tes

### Null Hypothesis, Alternate Hypothesis, Decision Rule...

For Exercises 1-3: (a) State the null hypothesis and the alternate hypothesis. (b) State the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding H0? (e) What is the p-value? Interpret it. 1. The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage

### Hypothesis, Null and Alternative, & P-values

Q1: What is a p-value in testing hypothesis? Q2: How does this p-value help us to decide to/not to reject a Null hypothesis? What might happen if we do not use this p-value in particular, when we are rejecting a Null hypothesis? Q3: What are the limits of these p-values to decide if we have made a right decision on reje

### T tests, confidence intervals

1. Explain the difference between testing a single mean, testing the difference between two means from an "independent sample" and testing mean differences from a "dependent sample". 2. Choose a variable. You will be comparing the means of two groups to each other. Your sample will consist of 12 subjects in each group. You ma

### Statistics -Show and explain five step hypothesis (Strategy)

1. A National retail chain has 7 different strategies (S1 to S7) to increase its sell. None of these strategies work all the time. In the past they have used these strategies equal number of times and the following table shows the number time each strategy worked successfully. At the significance level .05, examine if all of the

### two-tail hypothesis test for the breaking strength of a certain

PROBLEM # 3 A certain type of cable was advertised as having a breaking strength of 1000 pounds. A test of XX pieces of this cable was conducted and the mean breaking strength of this sample was XXX pounds with a sample standard deviation of XX pounds. Conduct a two-tail hypotheses test at alpha = .05 to determine if this samp

### Statistics - Test claim

16. A steel pipe fittings company claims that the yield strength of its non-tempered couplings is more variable than that of its tempered couplings. A random sample of nine tempered couplings has a standard deviation of 13.1 mega-pascals, and a similar sample of nine non-tempered couplings has a standard deviation of 25.4 mega-p

### Hypothesis Test

A legal researcher is studying the age distribution of juries by comparing them with the overall age distribution of available jurors. The researcher claims that the jury distribution is different from the overall distribution; that is, there is a noticeable age bias in jury selection in this area.The table shows the number of j

### Hypothesis Test

1. Given the following data from two independent samples from which the population standard deviation is known, conduct a two-tailed hypothesis test to determine if the first sample mean is smaller than the second sample mean, given a 0.01 level of significance. n1 = 42 n2 = 30 xbar1= 39 xbar2 = 25 sigma1=8 sigma2 = 6

### Statistic distribution

9.54 Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a stand

### Evaluate: Five Step Testing Hypothesis

The following sample data shows the quarterly earnings in millions for two US companies. Your research interest is finding if the average earnings for these companies are different. Justify your answer by doing a five step testing of the hypothesis at the 0.05-level of significance. Show all the steps of the calculations. Com

### Theoretical Issues About Testing of Population Mean

How do hypothesis-testing procedures differ for the population mean when the population standard deviation is known or unknown? What is the relationship between two-sided hypothesis tests for means and confidence intervals? Why would the population variability and the sample size affects the power of a test? How do the leve

### Central Limit Theorem and its implications in Hypothesis Testin

Q1: What do you remember from the CLT and it's implications? Please touch up on them. Q2: Please explain how this theory is used in testing hypothesis. Q3: What are confidence intervals telling us? Q4: What region under the normal curve corresponds to Researcher's confidence? Q5: What are the area under the 2 tai

### Testing Claims and Identification

Testing Claims (a) Write the claim mathematically and identify Ho and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.