Large sample test for population mean

Click For Summary
SUMMARY

The discussion centers on a hypothesis test for the mean compressive strength of a new concrete mix, specifically testing H0: μ ≤ 1350 kPa against H1: μ > 1350 kPa. A sample of 100 blocks yielded a mean compressive strength of 1356 kPa and a standard deviation of 70 kPa. The calculated Z-score is 0.8571, leading to a P-value of 0.1963, which is greater than the significance level of 0.05. Consequently, the null hypothesis cannot be rejected, indicating that it remains plausible that the blocks do not meet the specified compressive strength requirement.

PREREQUISITES
  • Understanding of hypothesis testing, specifically one-tailed tests.
  • Familiarity with Z-scores and P-value calculations.
  • Knowledge of standard deviation and its role in statistical analysis.
  • Basic proficiency in interpreting statistical results in the context of quality control.
NEXT STEPS
  • Study the Central Limit Theorem and its implications for large sample sizes.
  • Learn about confidence intervals for population means using sample data.
  • Explore the use of statistical software for hypothesis testing, such as R or Python's SciPy library.
  • Investigate the implications of Type I and Type II errors in hypothesis testing.
USEFUL FOR

This discussion is beneficial for statisticians, quality control engineers, and students in fields involving statistical analysis and hypothesis testing, particularly in materials engineering and construction.

Poke

Homework Statement


[/B]
A new concrete mix is being designed to provide adequate compressive strength for concrete blocks. The specification for a particular application calls for the blocks to have a mean compressive strength μ greater than 1350 kPa. A sample of 100 blocks is produced and tested. Their mean compressive strength is 1356 kPa and their standard deviation is 70 kPa. A test is made of H0:μ ≤1350 versus H1:μ>1350.

a. Find the P-value.
b. Do you believe it is plausible that the blocks do not meet the specification, or are you convinced that they do? Explain your reasoning.

Homework Equations


It is asking for Population Mean, with large sample (n=100)
H0:μ ≤1350 ; H1:μ>1350 ; μ0 = 1350

Z = \frac{Mean - μ0}{ \frac{\sigma}{\sqrt{n}} }

The Attempt at a Solution


As H1:μ> μ0 , Area to the right of Z

Z = 0.8571, between 0.8023 and 0.8051
so P = 1 - \frac{0.8023+0.8051}{2}
P = 0.1963 > 0.05 (5%) = \alpha

So we cannot reject H0, and we can only conclude the blocks do not meet the specification is plausible.

Am I doing it in a correct approach, and final answer correct? Thanks!
 
Physics news on Phys.org
It is possible, yes, you cannot exclude it.
 

Similar threads

Hypothesis test and finding type 2 error probability
  • · Replies 2 ·
Replies
2
Views
2K
Sampling Distribution Question
  • · Replies 1 ·
Replies
1
Views
2K
Test comparing the means of 2 water samples
  • · Replies 2 ·
Replies
2
Views
2K
Small sample test for the difference between two means
  • · Replies 1 ·
Replies
1
Views
2K
Small sample test concerning 2 means with different variances
  • · Replies 2 ·
Replies
2
Views
2K
Confusion between z and t values
  • · Replies 5 ·
Replies
5
Views
3K
Testing Hypotheses about Means and Proportions
  • · Replies 11 ·
Replies
11
Views
2K
Hypothesis testing, P-value, β-error, sample size for β<=0.1
  • · Replies 4 ·
Replies
4
Views
3K
High School How Can We Compare Two Means to Test the Effectiveness of Diet A on Weight Loss?
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad Test Hypotheses with sample of Binomial RV's
  • · Replies 3 ·
Replies
3
Views
2K