You received a batch of 20 bottles of electrolyte from a company, and one bottle

Question

You received a batch of 20 bottles of electrolyte from a company, and one bottle is mislabeled with missing Li+ molar concentration. You know the average molar concentration of the remaining 19 bottles is 1.25 M. You would like to test the hypothesis that the average molar concentration of Li+ in the sample you received is significantly smaller than 1.27 M. The population standard deviation of 0.05 M. What is the maximum Li+ molar concentration of electrolyte in the mislabeled bottle for you to reject the null hypothesis at =0.05? Giving your answers to three decimal places.

Explanation / Answer

One sample z test for population mean

You received a batch of 20 bottles of electrolyte from a company, and one bottle is mislabelled with missing Li+ molar concentration. You know the average molar concentration of the remaining 19 bottles is 1.25 M. You would like to test the hypothesis that the average molar concentration of Li+ in the sample you received is significantly smaller than 1.27 M. The population standard deviation is 0.05 M. What is the maximum Li+ molar concentration of electrolyte in the mislabelled bottle for you to reject the null hypothesis at =0.05? Giving your answers to three decimal places

Solution:

Here, we have to use the one sample z test for the population mean. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: µ = 1.27

Alternative hypothesis: Ha: µ < 1.27

We are given

Sample mean = 1.25

Sample size = n = 19

Population standard deviation = 0.05

Level of significance = alpha = 0.05

The one sample z test is given as below:

Z Test of Hypothesis for the Mean

Data

Null Hypothesis                       m=

1.27

Level of Significance

0.05

Population Standard Deviation

0.05

Sample Size

19

Sample Mean

1.25

Intermediate Calculations

Standard Error of the Mean

0.0115

Z Test Statistic

-1.7436

Lower-Tail Test

Lower Critical Value

-1.6449

p-Value

0.0406

Reject the null hypothesis

Here, we get p-value as 0.0406 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that the average molar concentration of Li+ in the sample is 1.27 M, this means we concluded that the average molar concentration of Li+ in the sample you received is significantly smaller than 1.27 M.

Z Test of Hypothesis for the Mean

Data

Null Hypothesis                       m=

1.27

Level of Significance

0.05

Population Standard Deviation

0.05

Sample Size

19

Sample Mean

1.25

Intermediate Calculations

Standard Error of the Mean

0.0115

Z Test Statistic

-1.7436

Lower-Tail Test

Lower Critical Value

-1.6449

p-Value

0.0406

Reject the null hypothesis

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