A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test \( H_0: \mu = 175 \) millimeters versus \( H_1: \mu > 175 \) millimeters, using the results of \( n \) samples. Find the boundary of the critical region if the Type I error probability is \( \alpha = 0.03 \) and \( n = 4 \).Round your intermediate values to two decimal places. Round your answer to one decimal place (e.g., 98.76).\[\bar{X} \geq\]

The hypotheses are:where is the foam height.The population standard deviation is millimeters.The…

Answered: A consumer products company is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A journal published a study of the surface roughness of water pipes. An instrument measured the surface roughness (in micrometers) of 40 sampled sections of coated interior pipe. Let x¯x¯ denote the sample mean. Assume that the surface roughness distribution has a mean of μ=1.65μ=1.65 micrometers and a standard deviation of σ=0.8σ=0.8 micrometers. Find the probability that x¯x¯ exceeds 1.75 micrometers. Select one: a. 0.2148 b. 0.2683 c. 0.3979 d. 0.4356
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Solve the problem and draw the normal curve with the shaded region representing the given scenario in the problem. The accountants of a known auditing firm have a mean daily salary Php 850 with a standard deviation of Php 82. Find the median and the mode, and compare it with the given mean value. Determine the intervals within 1, 2 and 3 standard deviations from the mean, that is, the µ ± 1σ, µ ± 2σ, µ ± 3σ. Verify that the empirical rule holds that is, approximately, 68%, 95%, and 99% of the data lie within ± 1σ, ± 2σ, ± 3σ units of the mean, respectively. If an accountant from the firm is chosen at random, what is the probability that he /she earning Php 950 to Php 1,000? What percentage of the accountants will fall in between the salary of Php 300 and Php 500?
You are studying the velocities of projectiles. Prior experience tells you that standard deviation of velocities is around 9.7 ft/sec. How many independent samples of projectile velocity do you have to measure to estimate the mean velocity within ±±0.98 ft/sec with 92% confidence?
A company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 66 residential customers has a mean monthly consumption of 900 kWh. Assume the population standard deviation is 123 kWh. At a = 0.10, can you support the claim? Complete parts (a) through (e). B. The critical value is 1.28 Identify the rejection region(s). Select the correct choice below. O A. The rejection regions are z 1.28 OB. The rejection region is z > 1.28 OC. The rejection region is z< 1.28. (c) Find the standardized test statistic. Use technology. The standardized test statistic is z = (Round to two decimal places as needed.)
(b) Find the critical value(s) and identify the rejection region.
A population of values has a normal distribution with μ=105.7μ=105.7 and σ=10.3σ=10.3. You intend to draw a random sample of size n=99n=99.What is the mean of the distribution of sample means?μ¯x=μx¯= What is the standard deviation of the distribution of sample means?(Report answer accurate to 2 decimal places.)
A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 924 milligrams. A random sample of 58 breakfast sandwiches has a mean sodium content of 918 milligrams. Assume the population standard deviation is 24 milligrams. At α=0.10, do you have enough evidence to reject the restaurant's claim? Complete parts (a) through (e). Also find the critical values.
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