Q5) a) A manufacturer of tennis balls claims that the Company controls the weights of the balls accurately so that their variance is not more than 1 mg². A random sample of 31balls yields variance of 1.62 mg² . Is this evidence sufficient to reject the claim at a 5% level of significance? b) A survey claimed that students in a certain university spend on an average more than 75 minutes a day on intermet. To check the validity of the claim a sample of 100 students from the university was taken. It revealed a mean of 80.23 minutes with a standard deviation of 45.67 minutes. i) Which test statistic would you use to test the above claim, explain ii) At the 2% level of significance, does the claim appear to be valid? iii) State the underlying assumption, if any. iv) Obtain the P-value of the test and interpret it. v) For the test above, what is the probability of Type II Error when, in fact, u = 80?

Q5) a) A manufacturer of tennis balls claims that the Company controls the weights of the balls accurately so that their variance is not more than 1 mg². A random sample of 31balls yields variance of 1.62 mg² . Is this evidence sufficient to reject the claim at a 5% level of significance? b) A survey claimed that students in a certain university spend on an average more than 75 minutes a day on intermet. To check the validity of the claim a sample of 100 students from the university was taken. It revealed a mean of 80.23 minutes with a standard deviation of 45.67 minutes. i) Which test statistic would you use to test the above claim, explain ii) At the 2% level of significance, does the claim appear to be valid? iii) State the underlying assumption, if any. iv) Obtain the P-value of the test and interpret it. v) For the test above, what is the probability of Type II Error when, in fact, u = 80?

Name: Q5) a) A manufacturer of tennis balls claims that the Company control
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Q5) a) A manufacturer of tennis balls claims that the Company controls the weights of the ballsaccurately so that their variance is not more than 1 mg². A random sample of 31balls yieldsvariance of 1.62 mg² . Is this evidence sufficient to reject th

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: Were the two laboratories measuring the same thing? (Assume normality and common variance.) Be sure…

Q: On the basis of data provided by a salary survey, the variance in annual salaries for seniors in…

A: Solution: Given information: n1=25 Sample size of seniors n2=26 Sample size of managerss21=2.1…

Q: An automobile manufacturer claims that its van has a 54.3 miles/gallon (MPG) rating. An independent…

A: From the provided information, Population mean (µ) = 54.3 miles/gallon Population variance (σ2) =…

Q: The data from an independent-measures research study produce a sample mean difference of 4 points…

Q: A machine makes drill bits. When the machine is operating correctly, the variance of the diameter of…

A: Null Hypothesis:H0:σ2≤0.04 inches. Alternative Hypothesis: H1:σ2>0.04 inches. Test statistic:…

Q: 5. A bolt manufacturer makes a type of bolt to be used in airtight containers. The manufacturer…

Q: On-The-Ball, Inc., makes ball bearing that are used in tractors and other equipment. On the 8-to-4…

Q: Assume thAt scores on a standardized test are known to follow a bell shaped distribution with a mean…

A: L

Q: 8) A soft-drink dispensing machine is said to be out of control if the variance of the contents…

A: Given n=25 Population variance=1.15 Sample variance=2.03

Q: Show that if a one-way analysis of variance is performed on the ranks of the observations instead of…

A: Ranking the Data- In the Kruskal-Wallis test, the original data is ranked across all groups. Each…

Q: In a study conducted on the variance of weights of bread produced daily in a bread factory, the…

A: the average weight of 51 breads was calculated as 400gr and variance as 700. the variance of bread…

Q: A researcher believes that the mean earnings of top-paid actors, athletes and musicians are the…

A: Denote μ1, μ2, and μ3 as the true mean earnings of to-paid actors, athletes, and musicians,…

Q: 1.A research conducted by a dietitian indicates that running increases the lifespan among African…

A: In hypothesis testing, there are always two hypotheses. These are null and alternative hypotheses.…

Q: By what numerical value should SS be divided in order to compute an unbiased variance?

A: The variance is obtained using ratio of squared deviations and sample size.

Q: A random sample of 23 bags of apples (marked as 10 pounds each) received by a large grocery chain…

A: Solution: State the hypotheses. Null hypothesis: That is, the true mean of all bags is not less…

Q: A teacher is interested in assessing whether or not there is the same amount of variance in the…

A: Given, A sample of 15 boys had variance 460 A sample of 13 girls had variance 1400

Q: 18) We conducted a linear regression analyses based on the full sample (note: more than the 8…

Q: An article included a summary of findings regarding the use of SAT I scores, SAT II scores, and high…

A: Coefficient of determination defines the variation in the response variable explained by the…

Q: A production manager of a company producing canned fruits claims that the mean weight of cans is…

Q: A company produces orange juice bottles with a volume of approximately 2 liters each. One machine…

Q: A researcher intends to estimate the effect of a drug on the scores of human subjects performing a…

A: From the provided information,Confidence level = 90%

Q: A production engineer wants to determine if two assembly lines are producing the same mean number of…

Q: if variances are unequal, which would be an alternate non-parametric test for the independent…

A: When the variances are unequal, Mann-Whitney U Test would be an alternate non-parametric test for…

Q: A school administrator wants to see if there is a difference in the number of students per class for…

A: The confidence interval measures the range where the true parameter occurs. It has two parts, they…

Q: A certain type of thread is manufactured with a mean tensile strength of 71.8 kilograms and a…

A: Solution Given That , A certain type of thread is manufactured with a mean tensile strength of 71.8…

Q: Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. H0:…

A: Given that Sample Variance 1 (s_1^2)(s12) = 10.710.7 Sample Size 1 (n_1)(n1) = 1515 Sample…

Q: The quality control department of a soup brand is concerned that its soups contain more MSG than the…

A: Hi! Thank you for posting the question. Since your question has more than three sub-parts, we have…

Q: The manager of computer operations of a large company wishes to study computer usage of two…

A: (a) That is, there is no evidence to conclude that there is a difference in the mean processing…

Q: Suppose an airline claims that its flights are consistently on time with an average delay of at most…

A: As per our policy, we can answer only 3 sub-parts of a question. If you want solution for other…

Q: Ex. Derive the MLE for a random sample from Exp(A) distribution that is subject to left truncation…

A: Solution:Let's assume that we have a random sample of size n from an exponential distribution with a…

Q: An article about “Relative Controllability of Dissimilar Cars” reported a study in which 14 subjects…

A: sample mean, x = 1.21 sample variance = 160.7824 sample standard deviation, s = 160.7824 = 12.68…

Q: which of the following excel functions would you use to answer this question "Is the number if…

A: We are asked about which test will be used for comparing the number of applications accepted for…

Q: A professor claims that the final exam grades are more widely dispersed in Principles classes…

A: Assume that the variance of final exam grades for Principal classes is σ12 and the variance of final…

Q: An automobile manufacturer claims that their van has a 50.5 miles/gallon (MPG) rating. An…

A: In given question,We know that ,for population : an automobile manufacturer claims that their van…

Q: An electronic company's records show that the mean number of circuit.boards rejected per batch is…

A: It is given that Sample size n = 10 Sample variance s2 = 2.5 Population variance = 1.4

Q: Find interquartile range for mileage data and value of variance

A: It is given that a sample of 9 cars, in hundreds of dollars is 10, 6, 8, 10, 5, 3.5, 7.5, 7, 9.5

Q: The amount of chlorine in 100 cm3 water taken from a water tank was measured, the average was 2.15…

A: Given Data: x¯=2.55s2=0.49n=100 Null and Alternate Hypothesis: H0: μ=2.15HA: μ>2.15

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

Q5) a) A manufacturer of tennis balls claims that the Company controls the weights of the balls
accurately so that their variance is not more than 1 mg². A random sample of 31balls yields
variance of 1.62 mg² . Is this evidence sufficient to reject the claim at a 5% level of
significance?
b) A survey claimed that students in a certain university spend on an average more than 75
minutes a day on intermet. To check the validity of the claim a sample of 100 students from
the university was taken. It revealed a mean of 80.23 minutes with a standard deviation of
45.67 minutes.
i) Which test statistic would you use to test the above claim, explain
ii) At the 2% level of significance, does the claim appear to be valid?
iii) State the underlying assumption, if any.
iv) Obtain the P-value of the test and interpret it.
v) For the test above, what is the probability of Type II Error when, in fact, u = 80?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers? Use α = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal. Teacher 1 Teacher 2 ?̅1 = 473 ?̅2 = 459 S1 = 39.7 S2 = 24.5 n 1 = 8 n 2 = 18 a. State the null and alternate hypotheses (write it mathematically) and write your claim. b. Find the test statistic c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and…
(3.) A system contains components connected in parallel as shown in the diagram. If all components operate inderentently, & each component has probability 0.45 of failing What is the minimum number of components that must be connected in parallel so that th Probability that the system operateds exceeds 0.9999? The minimun number of components that must be connected in parallel is.
A research conducted by SSTA022 Class representative at the University of Limpopo indicates that running increases the lifespan among African men. The mean lifespan of 31 African men runners was 34.0% more than the mean lifespan of 31 inactive African men, with variances reported to be 110.25% and 104.04%, respectively. Assuming the populations to be approximately normally distributed with equal variances.i) Can you conclude that there is a significant increase in the lifespan of the men runners over the inactive men at ? = 0.05? ii) Construct a 95% confidence interval for ?1 − ?2.
A study was performed concerning risk factors for carotid-artery stenosis (arterial narrowing) among 264 men. The data reported is: Sample size Mean Standard deviationGroup 1: No stenosis 156 5.3 1.4Group 2: Stenosis 108 5.1 0.8 The test stastistic F is assumed to be 3.06 to check the equal variance. Question: Suppose researchers want to test if there is a significant difference in mean blood-glucose level between men with and without stenosis considering the critical F test is 1.35 with a equal variance (pooled), what is the test statistic for this test ?
0. A high school principal claims that the variance in the GPA of students in the graduating class is Tess than 0.39. You test this claim by sampling 31 seniors and find their GPA have a variance or 0.21. Ho:o? Ha:o2 < 0.39 (Claim) = 0.39 Is there enough evidence to reject Ho and support the principal's claim at a 0.10 level of significance? ohs A. No, the test statistic x? B. No, the test statistic x2 = 16.154 is not in the rejection region with critical value 40.256 C. Yes, the test statistic x? D. No, the test statistic x2 = 21.434 is not in the rejection region with critical value 20.599 E. Yes, the test statistic x? = 16.154 is in the rejection region with critical value 20.599 = 20.599 is not in the rejection region with critical value 21.434 %3D 20.599 is in the rejection region with critical value 16.154 %D
A researcher intends to estimate the effect of a drug on the scores of human subjects performing a task of psychomotor coordination. The members of a random sample of 9 subjects were given the drug prior to testing. The mean score in this group was 9.07, and the sample variance was 17.68. An independent random sample of 10 subjects was used as a control group and given a placebo prior to testing. The mean score in this control group was 15.21, and the sample variance was 27.48. Assuming that the population distributions are normal with equal variances, find a 90% confidence interval for the difference between the population mean scores The confidence interval is<, -,O (Round to two decimal places as needed.)
The student will conduct a test of a single variance. Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. A sample standard deviation of 15 minutes is the same as a sample variance of ["", ""] minutes. find the a. Degrees of freedom = ["", ""] b. Chi2 test statistic = ["", ""] c. p-value =
Gestation period is the length of pregnancy, or to be more precise, the interval between fertilization and birth. In Syrian hamsters, the average gestation period is 16 days. Suppose you have a sample of 31 Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups, and who have an average gestation length of 17.1 days and a sample variance of 26.0 days. You want to test the hypothesis that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is sMM= a. 31, b. 0.5232, c. 0.7328, d. 0.9158. The t statistic is- a. 1.50, b. 2.10, c. 2.63, d. 1.20 Now suppose you have a larger sample size n = 95. Calculate the estimated standard error and the t statistic for this sample with the same sample average and the same…
Give a 99.8% confidence interval, for μ₁ −μ₂ given the following information. n₁ = 35, x₁ = 1 2.41, s₁ = 0.39 81 n₂ = 20, x₂ = 2.62, s₂ = 0.83 2 -0.21 ✓0.69 X Use Technology Rounded to 2 decimal places.
In a comparison between the mean waiting time of the patients in the hospitals of Giza and Alexandria governments the minister of Health randomly selected 60 hospitals from Giza government and their mean waiting time was 30 minutes and the previous reports showed that the variance was 10 minutes. Also a sample consist of 50 hospitals from Alexandria governments was selected and their mean waiting time of this sample was 15 minutes and from previous reports the variance was 5 minutes. 1-Construct the 95% C.I for the difference between the average waiting time in Giza & Alex2- Without any computations, discuss fully and precisely what will happen to the results you obtained in part (1) if the confidence level changed to be 99% instead of 95%. Give the reason for your answer
13
Suppose that 90% of Narnians are children, that Narnian children have normallydistributed BMIs with a mean of 25 kg/m2and variance of 64 (kg/m2) 2, and that Narnianadults have normally distributed BMIs with a mean of 30 kg/m2and variance of 100(kg/m2)2. WHO currently categorizes BMIs greater than 30 as obese.a. What is the prevalence of obesity among Narnian children?b. What is the prevalence of obesity among Narnian adults?c. What is the overall prevalence of obesity among Narnians?d. Are age and obesity statistically independent in Narnia?e. What proportion of Narnians are obese children?f. What proportion of obese Narnians are children?