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# Hypothesis Testing

### Standard Deviation

1. The Gibbs Baby Food Company wishes to compare the weight gain of infants using their brand versus their competitor's. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. The standard deviation of the sample was 2.3 pounds. A sample of 55 babie

### Statistics Conducted P-Values

A study conduced a few years ago claims adult men spend an average of 11 hours a week watching sports on tv. A recent sample of 100 adult men showed that the mean time they spend per week watching sports on TV is 9 hours. The population standard deviation is given to be 2.2 hours. a) Test at the 1% significance level whether

### Hypothesis testing and statistical significance.

In an article about anti-tobacco campaigns, Siegel and Biener (1997) discuss the results of a survey of tobacco usage and attitudes, conducted in Massachusetts in 1993 and 1995; Table 4-4 shows the results of this survey. Focusing on just the first line (the percentage smoking 25 cigarettes daily), explain what this result means

### Hypothesis Test - 5 Problems including t-test, z-test and ANOVA analysis

10.30 In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At &#945; = .01, did the yellow fire trucks have a signifi

### 3 problems

6. In 1978, a small plane slammed into a passenger jet over San Diego, killing 144 people. Langhorne Bond, then the head of the FAA, responded by proposing strict new curbs on small planes around many busy airports. Examine the following FAA data. Is there a statistically significant difference in the frequency of different

### General Statistics

1. Z-test A researcher wishes to test the claim that the average age of lifeguards in Ocean City is greater than 24 years. She selects a sample of 36 guards and finds the mean of the sample to be 24.7 years with a standard deviation of 2 years. Is there evidence to support her claim at a 95% level of confidence? 2. T-test fo

### Statistics: Calculate z scores and p values

Examples Fill in the answers for each table below. Please report your z scores to two decimals and your p values to three decimals. If the p value is less than .001, please report p < .001. µ=25 σ=2 X z p(z) 33 35 43 22 17 µ=25 σ=5 X z p(z) 33 35 43 22 17 µ

### Test the Hypothesis at Significance Level (Alpha)= 0.05

Test the hypothesis at the 0.05 level of significance. The treatment means are equal. Treatment 1 Treatment 2 Treatment 3 9 13 10 7 20 9 11 14 15 9 13

### Testing proportions: would you expect to observe this many people in favor of this proposition?

A survey dating back to the 1990's suggested that Americans anticipated a reduction in living standards and that a steadily increasing consumption no longer might be as important as it was in the past. (Were they right?) Suppose that a poll of 2000 people indicated 1373 in favor of forcing a reduction in the size of American

### Hypothesis Testing Widgets

You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 500 and a population standard deviation of 6 and a sample size of 18. Machine 2 has a sample mean of 500.5 and a population standard deviation of 2 with a sample size of 2. With an alpha of .05 can we claim that ther

### Hypothesis Testing: Mean Number of Customers

Your population mean has always been 9 customers per hour. The sample standard deviation is 4. The sample size is 25. The sample mean is 8. .05 is your level of significance. Use your sample data to test the claim that the number of customers you are serving per hour has changed. Choose the most accurate answer to running

### Proportion - Pro Life

If a random sample of 10 people found that 9 were pro-life (i.e., 90%), while another random sample of 1,000 people from the same population found that 550 were pro-life (i.e., 55%), which would you find more significant? Why?

### Infomercial claims - Statistics

Infomercials often peddle products under the guise of "studies show ..." While some of the products are surprisingly good, many are not. Why should you be suspicious of any products advertised on these shows, despite the seeming existence of data?

### Statistics Example Problem: Hypothesis Testing

In your work for a national health organization, you are asked to monitor the amount of sodium in a certain brand of cereal. You find that a random sample of 52 cereal servings has a mean sodium content of 232 milligrams with a standard deviation of 10 milligrams. At α = .04, can you conclude that the mean sodium content per se

### Statistics: Probing the Pollster for information about candidate conclusions

When pollsters report results of a poll, they often include the margin of error but not much more. If candidate X has 54% support of the voters with a margin of error of 3%, that means the candidate is predicted to have between 51% and 57% support in the election. Before jumping to conclusions, what other information would y

### Testing Claim of Delivery Within 15 Days

A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be 5.6 days. a. State the null and alternative hypotheses. b. Using a critical value

### Statistics: Mill Valley Brewery, bank manager's system, mean body temp

See attached file. Please show all work. Consider the following hypothesis test: Ho: mu &gt;= 80 Ha: mu &lt; 80 A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion (reject or fail to reject) for each of the following sample results. Use alpa = 0.01 1. x = 7

### Statistics: P value, Tri-Cities Tobacco, attribute vs variable control chart, note pads

9.8 Calculate the test statistic and p-value for each sample. a. H0: &#960; &#8804; .60 versus H1: &#960; > .60, &#945; = .05, x = 56, n = 80 b. H0: &#960; = .30 versus H1: &#960; = .30, &#945; = .05, x = 18, n = 40 c. H0: &#960; &#8805; .10 versus H1: &#960; < .10, &#945; = .01, x = 3, n = 100 9.12 The Tri-Cities Tob

### Statistics: Inferences from Two Samples about home size and selling price

See attached data file. Home Size and Selling Prices Using the sample data that is attached, 21 homes with living areas under 2000 ft(2) have selling prices with a standard deviation of \$32,159.73. There are 19 homes with living areas greater than 2000 ft(2) and they have selling prices with a standard deviation of \$66,628

### Statistics: Compare Variation in Two Samples of braking distances of cars

Braking Distances of Cars A random sample of 13 four-cylinder cars is obtained and the breaking distances are measured and found to have a mean of 137.5 ft and a standard deviation of 5.8 ft. A random sample of 12 six-cylinder cars is obtained and the braking distances have a mean of 136.3 ft and a standard deviation of 9.7 f

### Hypothesis Testing of Variance: Student and Faculty Car Ages

See attached file. Interpreting Display for Student and Faculty Car Ages. Students at the author's college randomly selected samples of student cars and faculty cars and recorded their ages based on the registration stickers. See the following excel display of the results. What is the P-value for a hypothesis test of e

### Inferences About Two Means: Independent Samples

Hypothesis Testing for Cigarette Tax: The mean tar content of a simple random sample of 25 unfiltered king size cigarettes is 21.1 mg, with a standard deviation of 3.2 mg. The mean tar content of a simple random sample of 25 filtered 100 mm cigarettes is 13.2 mg with a standard deviation of 3.7 mg. Use a 0.05 significance

### Step 5 of hypothesis testing: Calculating the value of Z

The purpose of Team C's research is to determine why men receive higher salaries than women. Before researching the topic, team c will verify that women do indeed make less than men. According to the wages data set, women consist of only 3 of the top 25 salaries out of 100 samples. The mean women's salary is \$24,452 with a stand

### Are the Population Means equal?

At the 10% level of significance, does the following sample evidence indicate that the two population means are equal? Assume the populations are normally distributed. Sample 1: n = 21 = 10 s = 2.15 Sample 2: n = 25 = 12 s = 3.90 HINT: Since both of the samples are small, you must first determine whether the two pop

A total of 61,647 people responded to an Elle/ MSNBC.com survey. It was reported that 50% of the respondents were women and 50% men. Of the women, 27% said that female bosses are harshly critical; of the men 25% said that female bosses are harshly critical. With this sample data with a 0.05 significance level to test the cla

Are Seat Belts Effective? A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed. Use this data with a 0.05 significance level to test the claim that the fatality rate is higher for

### Statistics

1. Assume that you plan to use a significance level of &#945; = 0.05 to test the claim that p1 = p2, Use the given sample sizes and numbers of successes to find the P-value for the hypothesis test. n1 = 100 n2 = 140 x1 = 41 x2 = 35 a. 0.4211 b. 0.0021 c. 0.0512 d. 0.0086 2. Construct the indicate

### Test a Claim About a Mean for weight loss: Sigma Not Known

Is the Diet Practical? When 40 people used the Weight Watchers Diet for one year, their mean weight loss was 3.0 lb and the standard deviation was 4.9 lb. Use a 0.01 significance level to test the claim that the mean weight loss is greater than 0 lb. Based on these results, does the diet appear to be effective? Does the diet app

### Hypothesis t testing problems

Question #1 / 9 The mean SAT score in mathematics is . The founders of a nationwide SAT preparation course claim that graduates of the course score higher, on average, than the national mean. Suppose that the founders of the course want to carry out a hypothesis test to see if their claim has merit. State the null hypothesis