### Hypothesis Testing and Statistical Analysis#### Calculating the P-value1. **Given:** - Sample mean \(\bar{X} = 1,340\) - Find the P-value (rounded to four decimal places). **P-value =** (Input box for answer)2. **Determine Rejection of Null Hypothesis:** - **Significance Level:** 0.01 - **Decision:** - ☐ Reject \(H_0\) - ☑ Do not reject \(H_0\)#### Probability Distribution of the Test Statistic- **Condition:** - Population mean \(\mu = 1,350\) - Sample size \(n = 13\)- **Distribution Options:** - ☐ The test statistic has a normal distribution. - ☐ The test statistic has a gamma distribution. - ☐ The test statistic has an exponential distribution. - ☑ The test statistic has a binomial distribution.#### Mean and Standard Deviation of the Test Statistic- **Calculate:** - **Mean:** (Input box) KN/m\(^2\) - **Standard Deviation:** (Input box) KN/m\(^2\)#### Type II Error Probability Calculation- **Condition:** - \(\alpha = 0.01\) - Probability of judging the mixture as unsatisfactory when \(\mu = 1,350\) (Type II error). **Probability =** (Input box for answer, rounded to four decimal places) **Title: Evaluating Compressive Strength for Grouting Mix****Introduction:**For effective grouting, it's essential to use a mixture of pulverized fuel ash and Portland cement that demonstrates a compressive strength exceeding 1,300 kN/m². This specification ensures structural integrity and safety.**Key Specifications:**- **Compressive Strength Requirement:** Greater than 1,300 kN/m².- **Usage Condition:** The mixture will only be applied if experimental evidence conclusively verifies that the specified strength is achieved.- **Statistical Analysis:** The compressive strength of this mixture is assumed to follow a normal distribution.**Parameters:**- **Standard Deviation (\( \sigma \)):** 63- **True Average Compressive Strength (\( \mu \)):** Denoted by \( \mu \).**Conclusion:**This guideline emphasizes rigorous testing to confirm the structural adequacy of the grouting mixture, ensuring it meets necessary safety and performance criteria.

Given information: μ=1300σ=63

Answered: If X = 1,340, find the P-value. (Round…

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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Find the probability that x will be less than 30. Round the answer to at least four decimal places. The probability that x will be less than 30 is…
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 91 86 80 107 99 108 86 89 The sample mean is x ≈ 93.3. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that ? = 12.5. The mean glucose level for horses should be ? = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use ? = 0.05. (a) What is the level of significance? b. (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since we assume that x has a normal distribution with known ?.The Student's t, since n is large with unknown ?. The standard normal, since we assume that x has a normal distribution with unknown ?.The standard normal, since we assume that x has a normal…
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 91 88 80 103 97 110 86 89 The sample mean is x ≈ 93.0. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that ? = 12.5. The mean glucose level for horses should be ? = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use ? = 0.05. (a)What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: ? > 85; H1: ? = 85; right-tailed H0: ? = 85; H1: ? < 85; left-tailed H0: ? = 85; H1: ? ≠ 85; two-tailed H0: ? = 85; H1: ? > 85; right-tailed (b)What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The…
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 95 88 80 107 101 108 84 87 The sample mean is x ≈ 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that ? = 12.5. The mean glucose level for horses should be ? = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use ? = 0.05. (a) Compute the z value of the sample statistic. (Round your answer to two decimal places.) (b) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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Page > of 3 The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 27.8 miles per gallon, with a standard deviation of 4.2 miles per gallon. Assume that a Normal model applies. Find the probability that a randomly selected automobile will average: 1. Less than 24 miles per gallon. 2. More than 19 miles per gallon. 3. Between 24 and 30 miles per gallon. 45°F Cloudy here to search (25
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose reading from the horse (in mg/100 mg). 92 87 82 107 99 109 85 89 The sample mean x-bar is 93.8. Let x be a random variable representing glucose readings taken from gentle Ben. We may assume x has a normal distribution, and we know from past experience that the standard deviation = 12.5. The mean glucose level for horses should be mu = 85mg/100gl. Do these data indicate that gentle Ben have a overall average glucose level higher than 85? Use alpha = 0.05 A- Compute z value of the sample stasistic test. Round answer to 2 decimal places B- Find (or estimte) the P-Value . Round answer to 4 decimal places I get 1.99 for the z value but cannot come up with correct p-value.
Assume the random variable X is normally distributed with mean = 50 and standard deviation σ = 7. Find the 77th percentile. Click the icon to view a table of areas under the normal curve. The 77th percentile is (Round to two decimal places as needed.) n example Get more help - Clear all Check answer
e average American man consumes 9.6 grams of sodium each day. ppose that the sodium consumption of American men is normally stributed with a standard deviation of 0.8 grams. Suppose an American nan is randomly chosen. Let X = the amount of sodium consumed. Round Al numeric answers to 4 decimal places where possible. %3D a. What is the distribution of X? X - N( b. Find the probability that this American man consumes between 9.5 and 10.6 grams of sodium per day. c. The middle 20% of American men consume between what two weights of sodium? Low: High:
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 95 86 82 The sample mean is x ≈ 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that o = 12.5. The mean glucose level for horses should be μ = 85 mg/100 ml. + Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H₁:μ >85; H₁: μ = 85; right-tailed 107 99 108 82 91 ⒸH₁: μ = 85; H₁: μ 85; two-tailed H₁: μ = 85; H₁: >85; right-tailed H₁: μ = 85; H₁₂ : μ< 85; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with unknown…

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