It is desired to determine what percentage of 60,000 young men in a city regularly exercise. For this purpose, a sample of 4000 young men was randomly selected, of which 1200 appears to be exercising regularly. Find the standard error of the sample rate.

Q: Use the t-distribution and the sample results to complete the test of the hypotheses.

A: The sample size is n = 100 Sample mean = 105.1 And sample SD = 15.5 Level of significance = 0.05

Q: (a) Prove that in sampling from a N(µ, o²) population, the sample mean is a consistent estimator of…

A:

Q: Whether the durability of a raw material is equal to a certain value 695 will be tested with…

A: It is required to test whether the durability of a raw material is equal to the given value or not.…

Q: From a population with a variance of 1296, a sample of 225 items is selected. At 95% confidence, the…

A: Given,sample size(n)=225standard deviation(σ)=1296=36α=1-0.95=0.05α2=0.025Z0.025=1.96     (from…

Q: Given a binomial random variable x and p = 0.2, find the mean for a sample size of 15.

A: Given data, p=0.2 n=15 What is the mean?

Q: For an ANOVA, when the null hypothesis is true, the F-ratio is balanced so that the numerator and…

A:

Q: d) If the variance is 120 1b, what sample size is necessary to estimate true yield point to be…

A: Given that  Variance  ?2=120 Margin of error =E =3 99% confidence.

Q: In testing the difference between the means of two independent populations, if neither population is…

A: Statistical inference is the theory of making the decision about the population parameters using…

Q: For an independent samples t-test what is the degrees of freedom?

A:

Q: The pooled variance value will be closer to whichever sample variance is larger, regardless of…

A: The pooled variance value will be closer to whichever sample variance is large, regardless of sample…

Q: With a large sample size such as n = 100, we do not need to assume the distribution is normal in…

A:

Q: In a 4-week study about the effectiveness of Do you Feel Better? using magnetic insoles to treat…

A: n1 = 52, x1 = 15, p1 = 0.288 n2 = 48, x2 = 18, p2 = 0.375

Q: For a one sample t-test with sample size 58, the degrees of freedom is:

A: Here AS PER POLICY I SHOULD HAVE TO CALCULATE FIRST MAIN QUESTION EVEN THOUGH I HAVE CALCULATED 2…

Q: For a population with σ = 12, how large a sample is necessary to have a standard error that is:…

A: What the standard error gives in particular is an indication of the likely accuracy of the sample…

Q: In a 4-week study about the effectiveness of Do you Feel Better? using magnetic insoles to treat…

A: The total n1=55 subjects wore magnetic insoles out of which only x1=15 subjects feel better. And…

Q: a. How many workers are there in each stratum? b. Estimate the mean forced vital capacity among the…

A: Here population is 1200(i.e. workers employing at a plant). Out of 1200 sample is taken of size 40.…

Q: Calculate how much difference is expected, on average, between two sample means if: n1 = 12, n2 =…

A:

Q: A travel agent claims that the average of the number of rooms in hotels in a large city is 500. At α…

A: It is given that the data for a random sample of seven hotels. The claim is that the average of the…

Q: In a 4-week study about the effectiveness of using magnetic insoles to treat plantar heel pain, 50…

A:

Q: If a sample of n = 4 scores is obtained from a normal population with µ = 70 and σ = 12, what is the…

A: Sample size, n = 4 Mean = 70 Standard deviation = 12 Sample mean = 69 (Raw score)

Q: Assume that you have a binomial experiment with p = 0.4 and a sample size of 120. What is the…

A: Given that, From binomial experiment, Probability, p = 0.4 Sample size, n = 120

Q: What sample size should be used in a study conducted to estimate the average monthly absences of…

A:

Q: The General Social Survey polled a sample of 1048 adults in the year 2010, asking them how many…

A: Answer :-  Z-test for two populations   1) when the data are normally follows then use the Z test (…

Q: A​ state-by-state survey found that the proportions of adults who are smokers in state A and state B…

A: Denote p1, p2 as the true population proportions of adult smokers in states A and B, respectively.

Q: The critical value for a 80% confidence inverval for a one sample proportion with a sample size of…

A: Solution: From the given information, the confidence level is 0.80.

Q: Calculate the P-value for a sample of 40 observations with a sample proportion of 0.6 if the null…

A:

Q: When calculating an independent-samples t test, the pooled variance is:

A: Given: Independent sample t-test.

Q: The standard error of a 16-unit sample of a variable with a mean of 20 and a variance of 64

A: Given data,Mean μ=20Variance σ2=64standard deviation =Varianceσ=64σ=8If n=16Standard error(σx)=?

Q: A sample of n = 26 scores is selected from a normally distributed population. State whether the…

A: The formula for Standard error is SE = σ/√n

Q: A record store owner finds that 15,0% of customers entering her store make a purchase. One morning…

A: Given,n = 188P = 0.15SE = ?

Q: In a 4-week study about the effectiveness of using magnetic insoles to treat plantar heel pain, 51…

A: (a) The null and alternative hypotheses are: Ho: p_1 = p_2Ho:p1​=p2​ Ha: p_1 \ne p_2Ha:p1​̸​=p2​…

Q: In general, increasing the sample size (for example, from n = 4 to n = 50) will  ---??Select??---…

A: We know that- Type I error is- Rejecting the true null hypothesis. By increasing the sample size,…

Q: Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of…

A: X be a random variable that follows binomial distribution with probability of success 0.40 and…

Q: Suppose that we will take a random sample of size n from a population having mean µ and standard…

A: It is given that the population mean is 559, the standard deviation is 0.3 and the sample size is…

Q: Use a 0.1 significance level to test the claim that the mean amount of delayed flight times between…

A: Let μ1 is defined as the mean amount of delayed flight time of Pink airlines, and μ2 is defined as…

Q: A telephone company claims that more than 15% of its customers have at least two telephone lines.…

A: It is given that Sample size n = 250 Number of customers who have at least two telephone lines, X =…

Q: For a hypothesis test comparing two Independent population means, the combined degrees of freedom…

A: given: hypothesis testing of comparison between two population mean  and population standard…

Q: simple random sample of size n=64 is obtained from a population that is skewed right with μ=77 and…

A:

Q: Opposing a random sample of size and equal 16A sample average of 185 it is observed the P value of…

A: Given sample size n = 16  and sample mean = 185  We have to find the p-value of the sample statistic…

Q: The assumption of homogeneity of variances was tested, and the Levene’s test yielded a value of (p =…

A: The hypothesis to be tested here is- H0:σ12=σ22=σ32=.....=σk2 Homogenity of varianceH1:σi2≠σj2 For…

Q: Suppose that we will take a random sample of size n from a population having mean µ and standard…

A: It is given that, Population mean,µ = 3 Population standard, σ = .6 Sample size, n = 8 According to…

Q: If you have samples of n1=19 and n2=17​, in performing the​ pooled-variance t​ test, how many…

A: Given,  n1=19 and n2=17

Q: For the specified margin of​ error, confidence​ level, and educated guess for the observed​ value,…

A: Zα/2 = 1.645  at α = 0.1 _____________________________ Use Excel function =NORMSINV(0.05) OR Z-…

Q: Assume that you have a binomial experiment with p= .3 and a sample size of a 100. The value of the…

A: Conider a binomial random variable "X". The variance of the random variable X is given by:

Q: Is the weight of Diet Coke less than the weight of Regular Coke? For the following test, assume…

A: Let μ1 is defined as the mean amount of the weight of Diet Coke, and μ2 is defined as the mean…

Q: To try to predict the outcome of the vote for the school board election, a town manager used random…

A: The correct option is option (A) "Yes, because it is a simple random sample"

Q: A large sample size is needed to show significance in a test of two population standard deviation. O…

A: False. Higher sample size allows the researcher to increase the significance level of the findings.…

Q: What is the sample variance and estimated standard error for a sample of n = 25 scores with SS =…

A: The random variable X follows normal distribution. We have to find the sample variance and standard…

Q: The claim is that for a smartphone​ carrier's data speeds at​ airports, the mean is μ=11.00 Mbps.…

A: Consider that μ defines the population mean smartphone carrier’s data speed at airport.   Null…

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.