Question

Yesterday in Turkey 35720 Covid19 tests have been conducted. 4789 of these tests turned to be positive. On April 9th, Thursday; 28578 Covid19 tests have been conducted. 4056 of these tests turned to be positive. At 0.01 significance level you want to check if the positive ratio has changed in 3 days? In this case what would be your test value?

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An engineer want to compare the performance of two machines.

Machine one produced average of 15 pcs/day in 10 days.

Machine two produced on the average 17 pcs/day in 12 days.

We know the standard deviations of these machines.The standard deviations are 2 pcs/day and 2.3 pcs/day respectively.

At %4 significance level, to test whether their means are equal or not; what would be calculated test statistics?

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Two different types of injection-molding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discolored. Two random samples, each of size 300, are selected, and 15 defective parts are found in the sample from machine 1 while 8 defective parts are found in the sample from machine 2. You want to test if it is reasonable to conclude that machine 2 produces less (difference is positive) fraction of defective parts, using α= 0.03. When you do the test In this case what would be your calculated test statistics?

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We would like to check if the standard deviations of two groups are same or not at 10% significance level. From first group 10 measurements are taken and sample standard deviation found to be 4. From second group (denominator) 15 measurements are taken and the standard deviation is found to be 5. After calculating test statistics and evaluating the critical values what would be your decision?

Answer 1

dear student, we can provide you with the solution of one question at a time.

1)

Test value Will be Z test statistic