n engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 9 engines and the mean pressure was 5.7 pounds/square inch with a variance of 0.81. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

The calculated t- value =  1.11 > 2.89 at 0.025 level of significance

Null hypothesis is rejected

The engineer designed the valve such that it would produce a mean pressure is not equal to  5.4

Step-by-step explanation:

Step(i):-

Given mean of the Population (μ) = 5.4

Given sample size 'n' = 9

Mean of the sample (x⁻) = 5.7

Standard deviation of the sample (s) = 0.81

Step(ii):-

Null Hypothesis: H₀:  The engineer designed the valve such that it would produce a mean pressure of 5.4

H₀: μ = 5.4

Alternative Hypothesis : H₁:  μ ≠ 5.4

Level of significance = 0.025

Test statistic

         t = 1.11

Degrees of freedom

ν = n-1 = 9-1 =8

t₀.₀₁₅ , ₈  = 2.89

The calculated t- value =  1.11 > 2.89 at 0.025 level of significance

Null hypothesis is rejected

The engineer designed the valve such that it would produce a mean pressure is not equal to  5.4

understand that i don't know the answers

will someone answer his question

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.