Question

It essential that the population of rebars to be used in a lightweight concrete application should have a yield strength of 17 psi. From the rebars delivered to the construction site by the supplier, the engineer ordered that a sample of 10 rebars to be randomly selected and tested for yield strength. The sample of 10 rebars yielded a value of 15.9 psi. Suppose it is known that yield strength is normally distributed and the variance of rebar strength is 5.0 psi.

a) Which specific statistical inference method(s) can be used to assess whether the rebars delivered to the construction site can be used in a lightweight concrete application? State how you chose this method. Provide a concise justification of your rationale.

b)Assess whether the rebars delivered to the construction site can be used in a lightweight concrete application using the seven-step method using the �-value method and a significance level of 0.05.

c)Develop and interpret the confidence interval linked to your analysis in 2(b).

d)If the true yield strength of rebars is 18 psi, what is the probability that the test will fail to capture this shift in the mean?

Answer 1

Given Information:

Population mean = 17 psi

Sample size = 10

Sample mean = 15.9 psi

Variance = 5 psi

Standard Deviation = square root of variance = 2.236 psi

A) Two-tail one sample z test will be used. This test compares whether the sample mean equals the population mean

B)

Step 1: Null hypothesis

Ho: The sample mean is equal to the population mean

Step 2: Alternate Hypothesis

Ha: The sample mean is not equal to the population mean

Step 3: Set up the level of significance

The level of significance level (alpha value) is assumed to be 0.05

Step 4: Deciding the test statistic

Two tail one sample z test will be used to test the claim

Following formula can be used to calculate the test statistic

Where,

X is the sample mean

Z is the z score

σ is the standard deviation

n is the sample size

u = population mean

Step 5: Calculating the test statistic

Step 6: Finding the p-value

By referring to the standard normal table, the p-value at z = -1.55 is 0.1211

Step 7: Conclusion

Since the p-value is more than the significance level, the null hypothesis will be accepted.

Therefore, the sample means and population mean are equal.

C) Confidence interval

Following formula can be used to calculate the confidence interval:

The value of z at a 95% confidence interval is 1.96

D) To calculate the probability, we need to calculate the z score first

By referring to the normal table, the probability at z = 1.414 is 0.0786

Therefore, the probability that the test will fail to capture the shift in mean is 0.0786