A manufacturer claims that the mean lifetime,  μ , of its light bulbs is  55  months. The standard deviation of these lifetimes is  6  months. Forty-two bulbs are selected at random, and their mean lifetime is found to be  58  months. Assume that the population is normally distributed. Can we conclude, at the  0.05  level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from  55  months? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: H0:   The alternative hypothesis: H1:   The type of test statistic: (Choose one)ZtChi squareF             The value of the test statistic: (Round to at least three decimal places.)   The two critical values at the  0.05  level of significance: (Round to at least three decimal places.) and Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 55 months?   Yes     No

Q: (b) Test the hypothesis at the a = 0.10 level of significance. Is a mean math score of 530…

A: H0 : ? =523 H1 : ? >523 Population mean = ? = 523 Sample S.D = s =116 Sample size = n…

Q: The average U.S. adult weight is 180 lbs. with a standard deviation of 15 lbs. A nutritional…

A: Given: X=Weight of US adult. Sample mean, x=165 Sample size, n=100 Population mean, μ=180 Standard…

Q: A pharmaceutical company produces pills of dose level of 40 mg. To maintain the quality control, the…

A: From the provided information, Population mean (µ) = 40 Population standard deviation (σ) = 0.4…

Q: Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 530 and a…

A: The objective of the question is to find the percentage of people taking the GRE who score within…

Q: A math teacher claims that she has developed a review course that increases the scores of students…

A:

Q: A math teacher claims that she has developed a review course that increases the scores of students…

A: Hypothesis testing is a way to test a claim about a population parameter.

Q: A math teacher claims that she has developed a review course that increases the scores of students…

A: Since you have posted multiple questions, we are answering the first question.

Q: A math teacher claims that she has developed a review course that increases the scores of students…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean…

A: Given information: For method A,μ=28σ=2For method B,μ=32σ=1

Q: A math teacher claims that she has developed a review course that increases the scores of students…

A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks   Sample Mean…

Q: The head of institutional research at a university believed that the mean age of full-time students…

A: The random variable age follows normal distribution. The population mean is 27.4 years. We have to…

Q: For a standardized psychology examination, the scores have a mean of 500 and a standard deviation of…

A: The following information is provided. Let X represents the scores of psychology examination.…

Q: A math teacher claims that she has developed a review course that increases the scores of students…

A: a.   Denote μ as the population mean math score.

Q: ccording to 2014 data from the Centers for Disease Control and Prevention, the average life…

A: Given: n=45 X=45.2σ=16.5

Q: A random sample of 88 eighth grade students' scores on a national mathematics assessment test has a…

A: Given Information: Sample size (n) = 88 Sample mean (x¯) = 293 Hypothesized value of population mean…

Q: The P-value for this hypothesis was found to be:

A: The test statistic is, z=x¯-μσn=78-682025=104=2.5 The test statistic is 2.5.

Q: Pilots who cannot maintain regular sleep hours due to their work schedule often suffer from…

A: Answer Sample size [n] =28Standard deviation =1.7Variance [1.7]^2 =2.89

Q: A study by researchers at a university addressed the question of whether the mean body temperature…

A: Given that, A study by researchers at a university addressed the question of whether the mean body…

Q: An industry has 2 factories, A and B. A sample of 300 workers is taken, with an average age of 17…

A: Given Data : For Sample 1 x̄1 = 17.0 σ1 = 6.9 n1 = 300 For Sample 2…

Q: Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random…

A: Assume that σ is the population standard deviation of volume of soda cans.

Q: A math teacher claims that she has developed a review course that increases the scores of students…

A: a) H0: μ = 514 , H1 > 514 ____________________________________

Q: The combined SAT scores for the students at a local high school are normally distributed with a mean…

A: Given : The combined SAT scores for the students at a local high school are normally distributed…

Q: A math teacher claims that she has developed a review course that increases the scores of students…

A:

Q: The brain volumes (cm³) of 50 brains vary from a low of 904 cm³ to a high of 1486 cm³. Use the range…

A: The minimum and maximum observation of the dataset are given as:The exact value of standard…

Q: A bottled water distributor wants to determine whether the mean amount of water contained in…

A:

Q: The average person spends a mean amount of $10.20 on coffee per week. You are interested to test if…

A: Given that   x̄ = 12.41 ,  μ = 10.20 , s = 5.25 , n= 31

Q: A math teacher claims that she has developed a review course that increases the scores of students…

A: The sample size is 2200, sample mean is 530, sample standard deviation is 119.

Q: A manufacturer claims that the mean lifetime, H, of its light bulbs is 54 months. The standard…

A:

Q: Consider a dataset containing the heights of 38 females who said they prefer to sit in the front of…

A: Givensample size(n)=38Mean(x)=62standard deviation(s)=2.5significance level(α)=10%=0.10The null and…

Q: A psychologist wants to test whether there is any difference in puzzle-solving abilities between…

A:

Q: The concentration of benzene was measured in units of milligrams per liter for a simple random…

A:

Q: The Challenger Disaster. In a letter to the editor that appeared in the February 23, 1987, issue of…

A: a.Probability that none of the “critically 1” items would fail is given by:

Q: An ecologist is studying the impact of local polluted waters on the growth of alligators. The length…

A: Length of adult male alligators follows a normal distribution with µ and standard deviation 2. n…

Q: Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean…

A: It is given that For Method A :  Mean (μ1) = 35Standard Deviation (σ1) = 3 For Method B : Mean (μ2)…

Q: A math teacher claims that she has developed a review course that increases the scores of students…

A: We have given that  Sample size n =2200 Sample mean =525 Standard deviation =110

Q: on of the length is 0.02 inch. At periodic intervals, a sample is selected to determine whether the…

A: Let X1 be the random variable such that  paper length x̅ : Sample mean of  paper length σ :…

Q: Fail to reiect H. There is sufficient evidence that the mean amount is different from 10

A: Given that  Sample size n =45 Sample mean=0.995 Standard deviation =0.006

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.