Two-sample t procedure. Two different alloys are being considered for making lead-free solder used inthe wave soldering process for printed circuit boards. A crucial characteristic of solder is its melting point,which is known to follow a Normal distribution. A study was conducted using a random sample of 21pieces of solder made from each of the two alloys. In each sample, the temperature at which each of the21 pieces melted was determined. The mean and standard deviation of the sample for Alloy 1 were X1218.9°C and $ = 2.7ºC; for Alloy 2 the results were X2 = 215.5ºC and $2 = 3.6ºC. If we were to test Ho:Hi = Hz against Hạ: H1 # H2, what would be the value of the test statistic??

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Answered: Two-sample t procedure. Two different…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of u = 67 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm). 59 51 76 38 65 54 49 62 68 55 64 67 63 74 65 79 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) X= cm S= cm (ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada. (a) What is the level of significance? State the null and…
200 people were randomly sampled and asked what they regularly eat for breakfast or lunch. Each person was identified as either a consumer or a non consumer of high-fiber cereals, and the number of calories consumed at lunch was measured and recorded. These data are summarized below; Consumer of high fiber cereals Non consumer of high fiber cereals η1 =41 η2 = 159 Mean 1 =603 Mean 2 =639 Stanadard deviation 1 = 110 Standard deviation 2 = 141 If the scientist claims that people who eat high fiber cereals for breakfast do consume on average fewer calories for lunch than people who don’t eat high fiber cereals for breakfast, and if it is true, high fiber cereal manufacturer will be able to claim another advantage of eating their products-potential weight reduction for dieter. REQUIRED Are there sufficient evidence at 5% significance level to support the above claim?
The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require that variability measurements on the population of all blades not exceed ?2 = 0.18 mm2. An engine inspector took a random sample of 81 fan blades from an engine. She measured each blade and found a sample variance of 0.28 mm2. Using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced? (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) Find or estimate the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.00 Find a 90% confidence interval…
A researcher wonders whether the recession has changed variability in family size in his city. Before the recession, the mean was 3.7 and the standard deviation was 1.76. The researcher randomly selects 41 families from a population that is normally distributed. His sample has a mean of 3.1 and a standard deviation of 1.45. Test the claim that the standard deviation in size has changed at the αα=.05 significance level.
A researcher wants to determine if there is a significant difference in the average math scores of two different teaching methods (Method A and Method B). He collects a sample of 50 students from each teaching method and calculates their scores. The sample mean score for Method A is 85 and the sample mean score for Method B is 80. The sample standard deviation for Method A is 4 and the sample standard deviation for Method B is 3. Conduct an independent samples t-test to determine if there is a significant difference in the average math scores of the two teaching methods at a significance level of 0.01.
A company manufactures an electrical cooling fan. When the fans are performing properly, samples of 200 fans average 12.5 watts with an average range of 1.2 watts. A 3σ control chart program is being used to monitor the performance of the fans, and these data from the 10 most recent samples were collected: Sample Number Sample Mean Sample Range 1 12.5 1.1 2 12.45 1.2 3 12.55 0.9 4 12.50 0.8 5 12.45 0.9 6 12.60 1.0 7 12.48 1.4 8 12.46 1.1 9 12.56 0.9 10 12.48 0.8 Compute the 3σ control limits and center line for an ⁻x chart. Compute the 3σ control limits and center line for an R chart. Plot the sample data on the ⁻x and R charts and decide if the performance of the fan is in control.
In a class of twenty-five 15-year old girls the average height is M = 62.60 inches. The national average for girls at this age is reported as follows: µ = 63.80 inches with a standard deviation, s = 2.66 inches. 1. What is the effect size Cohen’s d and what does it tell us about the effect? 2. Compute the z-statistic.
5a.) Draw the graphs. Round your final answers up to 6 decimal places, if applicable. Give the correct units.
The corrosive effects of various soils on coated and uncoated steel pipe was tested by using a dependent sampling plan. The data collected are summarized below, where d is the amount of corrosion on the coated portion subtracted from the amount of corrosion on the uncoated portion. Does this random sample provide sufficient reason to conclude that the coating is beneficial? Use ? = 0.01 and assume normality. n = 36, Σd = 227, Σd2 = 6244(a) Find t. (Give your answer correct to two decimal places.)(ii) Find the p-value. (Give your answer correct to four decimal places.)(b) State the appropriate conclusion. Reject the null hypothesis, there is significant evidence that the coating is beneficial.Reject the null hypothesis, there is not significant evidence that the coating is beneficial. Fail to reject the null hypothesis, there is significant evidence that the coating is beneficial.Fail to reject the null hypothesis, there is not significant evidence that the coating is beneficial.
The void volume within a textile fabric affects comfort, flammability, and insulation properties. Permeability of a fabric refers to the accessibility of void space to the flow of a gas or liquid. An article gave summary information on air permeability (cm3/cm2/sec) for a number of different fabric types. Consider the following data on two different types of plain-weave fabric: Fabric Type Sample Size Sample Mean Sample Standard Deviation Cotton 10 51.41 0.75 Triacetate 10 132.15 3.59 Assuming that the porosity distributions for both types of fabric are normal, let's calculate a confidence interval for the difference between true average porosity for the cotton fabric and that for the acetate fabric, using a 95% confidence level. Before the appropriate t critical value can be selected, df must be determined: df = 0.5625 10 + 12.8881 10 2 (0.5625/10)2 9 + (12.8881/10)2 9 = 1.8092 0.1849…
The titanium content of steel is determined in two laboratories by means of atomic absorptionspectrometry. The following data were obtained: Lab 1 0.470 0.484 0.463 0.449 0.482 0.454 0.477 0.409 Lab 2 0.529 0.490 0.489 0.512 0.486 0.502 - - A. Determine the variance of the measurement data obtained in the two laboratories.B. Is there any significant difference between these variances?
Use the IQR to determine if any of the data in the data set are outliers. {23,80,43,23,0,20,23,23,20,28}{23,80,43,23,0,20,23,23,20,28} Any data value less than or greater than

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