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# Z-Test

### Hypothesis Testing: Two sample Z test for proportion

1.To compare the effectiveness of two treatments 1 and 2 for a particular disease. Patients were separated in 2 treatment groups. A patient in group 1 received treatment 1 and patients in group 2 received treatment 2. The results are given in the table below: Treatment 1 Treatment 2 Success 170 180 Failure 30 10 (a) To

### Z-Test Flavors

A bubble gum company claims that the flavor in their gum lasts for at least 45 minutes. However, George has done 45 tests, and determined that his flavor lasted 40 minutes on average, with a sample standard deviation of 15. Do an exact statistical test on the claim, with alpha = 0.01.

### Study to determine drinking behavior of students

The University of Arkansas conducted a study to determine the drinking behavior of their students. They looked at 2 populations, students who lived on campus versus students who did not live on campus. They want to know if there is a difference in the drinking behavior between the 2 groups (use 95% level of confidence)

### Converting standard scores

Why it is possible to easily convert standard scores from one scale to another. When using these score listed below the mean and standard deviation of each of the transformed scores and the theoretical rationale for their equivalency for an example. Person A z-score of 1.0 CEEB Score = 600 IQ Score = 115 AP Score = 82%

### Statistics: Length of time to do a complete full service oil change at Speedy-Lube (z scores)

Please provide a very detailed explanation. The length of time to do a complete full service oil change at Speedy-Lube is normally distributed with a mean of 15.8 minutes and a standard deviation of 2.2 minutes X P(X < x) P(X > x) Mean Std dev 11 .0146 .9854 15.8 2.2 15 .3581 .6419 15.8 2.2 21 .9910 .0090 15.8 2.2 2

### Z Test of data for average GPA of students.

Data shows the average GPA of students at a school is 2.9. The GPA of a random sample of 16 biology students is 3.1 (with sample standard deviation= 1.2) Is the GPA of the biology students different from the general student body? Identify and justify the statistical procedure. Show all steps to test the hypothesis and in

### Z score for 1960: Peak discharge from a hydroelectric project in Wisconsin

The following table presents a data file that lists the peak discharge from a hydroelectric project in Wisconsin for the years 1957 to 1968. The variable peak discharge has an interval level of measurement. Year Peak Discharge 1957

### Population blood pressure (BP) of patients

1. Population blood pressure (BP) of patients is normally distributed, with a mean of 127, and standard deviation of 8. A random sample of 49 patients in the hospital found an average BP of 125. Find the z score test value, list the critical values (alpha = 5%), and indicate the hypothesis test results for a a) one-tailed (rig

### Statistics: Normal curve, normal distribution, probability, standard deviation, z-score. Finding area under a curve between two z-scores.

Please find below some problems to be solved. 1. Find the area of the indicated region under the standard normal curve. The area between z=0 and z=1.1 under the standard normal curve is _________. (Round to four decimal places as needed.) 2. Find the area of the indicated region under the standard normal curve. The area b

### Test statistic: Comparing two population proportions

A sample of 1545 men and an independent sample of 1691 women were used to compare the amount of housework done by men and women in dual-earner marriages. The study showed that 67.5% of the men felt that the division of housework was fair and 60.8% of the women felt the division of housework was fair. Is the proportion of men who

### Z test for two population proportions

A clinical trial is conducted comparing a new pain reliever for arthritis to a placebo. Participants are randomly assigned to receive the new treatment or a placebo and the outcome is pain relief within 30 minutes. Is there a significant difference in the proportions of patients reporting pain relief? Run the test at a 5% level

### Compute z-scores given populations and sample size

For a population with a mean of 60 and a standard deviation of 24, find the z-score corresponding to each of the following samples. a. M = 63 for a sample of n = 16 scores b. M = 63 for a sample of n = 36 scores c. M = 63 for a sample of n = 64 scores A population of scores forms a normal distribution with a mean of 40

### Z test for propotion

Babsie is a public affairs specialist at Park University. A press release issued by Babsie based on some research claims that Park University students study at least as much as the national average for students at four year universities. Across the nation, 73 percent of all students at four year universities study at least four

### Z-Score and Probability

1. An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which ball bearings can operate are 0.74 inch and 0.76 inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally di

### Find the z-score for the following values of x

Suppose a normal distribution has Find the z-score for the following values of x. u=1.5 and a=0.3 a. 2.3 b. 1.7 c. 2 d. 1.9 e. 2.1

### Statistics: Report on mean amount spent for lunch in company cafeteria.

A company is interested in estimating the costs of lunch in their cafeteria. After surveying employees, the staff calculated that a 95% confidence interval for the mean amount of money spent for lunch over a period of six months is (\$780, \$920). Now the organization is trying to write its report and considering the following

See attached chart. Your assistance is greatly appreciated. Thank you. TASK You have been provided the z-scores of three individuals. 1. Person A received a z-score of 1.0. 2. Person B received a z-score of 0 3. Person C received a z-score of -1.0. Using Figure above (see attchement), indicate each individual's sco

### Z score probability

Setting µ = 60 and &#963; = 7 What is the z score of 78? What is the z score of 45? What is the probability of 59? What is the probability of 62? What score falls at z = 1.64? What score falls at z = -1.96? What percentage of scores are 73 or less? What proportion of scores is between 45 and 78?

### Probability from Z score

The lifetime of a super tough AAA battery is normally distributed wit mean of 28.5 hours and standard deviation of 5.3 hours. For a battery selected at random, what is the probability that the lifetime will be? Use given data, requirement and sketch of normal curve labled to solve; a) 25 hours or less b) 34 hours or more

### Statistics: Grumney Family, MacBurger, National Safety Council, Chicken Delight

1. At the time she was hired as a server at the Grumney Family restaurant, Beth Brigden was told, "You can average at least \$20 a day in tips." Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was \$24.85, with a standard deviation of \$3.24. Can Ms. Brigden be 99% confident that

### Hypothesis Test: Z-Test for Two Sample Means

A sample of 40 observations is selected from one somewhat normal population. The sample mean is 102 and the sample standard deviation is 5. A sample of 50 observations is selected from a second source. The sample mean was 99 and the standard deviation was 6. Conduct a test of the hypothesis using the .04 level of significanc

### Z test for two populations: Hurricanes that strike the USA

From 1990-1998 there were 68 Atlantic hurricanes, or which 19 struck the US. From 1999-2006 there were 70 hurricanes, of which 45 struck the US. Does this evidence convince you the percentage of hurricanes that strike the US is increasing? Use a .01 significance level.

### Z-Test (Two Sample Means)

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 Alpha = .01, did the yellow fire trucks have a significantly lo

### Evidence of Increasing hurricane strikes in the US?

From 1990-1998 there were 68 Atlantic hurricanes, or which 19 struck the US. From 199-2006 there were 70 hurricanes, of which 45 struck the US. Does this evidence convince you the percentage of hurricanes that strike the US is increasing?

### Statistics: How to conduct a z test

A new company is manufacturing light bulbs. The CEO claims that the average light bulb lasts 260 days. A researcher selects 25 bulbs for testing. The sample bulbs last an average of 250 days with a standard deviation of 20 days. If the CEO's claim was true, can we conclude that 25 random bulbs will last 260 days at a 0.01 level

### Use Statistics for support explanation for average sales decreases

Historically, monthly sales for product X has been averaging \$30M with a standard deviation of \$2M. Last month sales decreased to \$28.5M, should you be concerned that sales are decreasing. Try to you use statistics to support you explanation.

### Toby's Truck Company and Statistical Analysis

Toby's trucking company determined that the distance traveled per truck per year is normally distrinuted, with a mean of 50.0 thousand miles and a standard deviation of 12.0 thousand miles. a. What proportion of trucks can be expected to travel between 34.0 and 50.0 thousand miles in the year? b. What percentage of trucks ca

### Statistics: Calculate z-scores for each student's test grades

One professor teaches a large section, section A, of a particular class, and on the first test of the term, the test scores in section A were approximately normally distributed with a mean of 78 and a standard deviation of 6. Another professor also teaches a large section, section B, of the same class, and on the first test of t

### Independent or Dependent Samples, Z-test, Critical Value

1. Classify as independent or dependent samples: The average price of gasoline at ten local stations, and the average price of gasoline at ten stations in another state. independent dependent 2. Classify as independent or dependent samples: The number of crimes committed in Pittsburgh, and the number of

### Finding Variables From Z-Scores

Assuming that the Z-scores are normally distributed with a mean u = 0 and a standard deviation sigma = 1.0 and if: a. P (0<z<a) = 0.3212 + n/100, find a? b. P (-b<z<b) = 0.3182 - n/100, find b? Note: if the number is not in the table use the nearest number in the table.