The strength limit of a specific type of a cable is random variable with mean value...

The strength limit of a specific type of a cable is random variable with mean value of 1500 kg and standard deviation 175 kg. The factory that manufactures this type of cables claims that they improved the materials that they used and the new resistance limit of the cable has increased. We randomly chose a sample of 50 cables and the mean strength limit was 1570 kg. If the strength limit in the specific type of cable is normally distributed with a significance level of 0.05, can we state that the claim of the manufacture factory is true? Justify your answer.

Solutions

Expert Solution

n=50, =0.05, =175, = 1500, = 1570

Ho : = 1500

Ha : > 1500

formula for test statistics is

z= 2.828

test statistics =2.828

now calculate P-Value

P-value = 1 - P(z < 2.828)

P(z < 2.83)= 0.9977

P-value = 1 - 0.9977

P-value = 0.0023

Rule for decision is

Reject Ho if (P-Value) ( )

here (P-Value = 0.0023) ( = 0.05)

Hence,

Reject the null hypothesis(Ho).

Therefore there is enough evidence to support the claim that the resistance limit of the cable has increased.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

6.2% of cable boxes of a certain type are defective. Let the random variable X represent...

6.2% of cable boxes of a certain type are defective. Let the random variable X represent the number of defective cable boxes among 200 randomly selected boxes of this type. Suppose you wish to find the probability that X is equal to 8. (i) Does the random variable X have a binomial or a Poisson distribution? How can you tell? (ii) If X has a binomial distribution, would it be reasonable to use the Poisson approximation? If not, why not?

1. There is a lower limit but no upper limit for a random variable that follows...

1. There is a lower limit but no upper limit for a random variable that follows the a. uniform probability distribution. b. exponential probability distribution. c. normal probability distribution. d. binomial probability distribution. 2. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What is the minimum weight of the middle 95% of the players? a. 196 b. 190 c. 151 d. 249 3. A scatter diagram reveals...

Determine whether the value is a discrete random variable, continuous random variable, or not a random...

Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of bald eagles in a countrynumber of bald eagles in a country b. The number of points scored during a basketball gamenumber of points scored during a basketball game c. The response to the survey question "Did you smoke in the last week question mark "response to the survey question "Did you smoke in the last week?" d. The number...

,,1-The sampling distribution of the mean is...............? 2- The expected value of a random variable corresponds...

,,1-The sampling distribution of the mean is...............? 2- The expected value of a random variable corresponds to the notion of the ________ of a sample.? 3- A negative correlation coefficient indicates a linear relationship between variables where one variable increases as the other increases. Is T or F? 4- If a variable is removed from the regression model when the t-statistic is lesser than 1, ________.? 5- If we sample with replacement from a finite population, the sampling distribution of the...

The inside diameter of a randomly selected piston ring is a random variable with mean value...

The inside diameter of a randomly selected piston ring is a random variable with mean value 11 cm and standard deviation 0.06 cm. (a) If X is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of X centered and what is the standard deviation of the X distribution? (Enter your standard deviation to five decimal places.) center cm standard deviation cm (b) Answer the questions posed in part (a) for...

Let X be a continuous random variable following normal distribution with mean value of: (a is...

Let X be a continuous random variable following normal distribution with mean value of: (a is 1) and standard deviation of b is 1/10 ,  What is the mode of X? (1 mark)  What is median of X? (1 mark)  What is ?(? > ?)? (1mark)  What is ?(? − ? < ? < ? + ?)? (1 mark)  What is ?(? − 1.96? < ? < ? + 1.96?))? (1mark)

The inside diameter of a randomly selected piston ring is a random variable with mean value...

The inside diameter of a randomly selected piston ring is a random variable with mean value 15 cm and standard deviation 0.07 cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.) (a) Calculate P(14.99 ≤ X ≤ 15.01) when n = 16. P(14.99 ≤ X ≤ 15.01) = (b) How likely is it that the sample mean diameter exceeds 15.01 when n = 25? P(X ≥ 15.01) =

4. Determine the x value if X is a normal random variable with mean 40 and...

4. Determine the x value if X is a normal random variable with mean 40 and standard deviation 6. a) ?(? > ?) = 0.5 b) ?(? > ?) = 0.28 c) ?(? < ?) = 0.82

Let X be a continuous random variable following normal distribution with mean value of: (a is...

Let X be a continuous random variable following normal distribution with mean value of: (a is the last digit of your student number) and standard deviation of b (b is the last digit of your student number divided by 10), a=9 b=9/10 What is the mode of X? What is median of X? What is P(X>a)? What is P(a-b<X<a+b)? What is P(a-1.96b<X<a+1.96b)?

A certain type of thread is manufactured with a mean tensile strength is 78.3kg, and a...

A certain type of thread is manufactured with a mean tensile strength is 78.3kg, and a standard deviation is 5.6kg. Assuming that the strength of this type of thread is distributed approximately normal, find: a) The probability that the mean strength of a random sample of 10 such thread falls between 77kg and 78kg. b) The probability that the mean strength greater than 79kg. c) The probability that the mean strength is less than 76kg. d) The value of X...

Subjects