Question

1. Consider a multinomial experiment with n = 245 and k = 4. The null hypothesis...

1.

Consider a multinomial experiment with n = 245 and k = 4. The null hypothesis to be tested is H0: p1 = p2 = p3 = p4 = 0.25. The observed frequencies resulting from the experiment are: (You may find it useful to reference the appropriate table: chi-square table or F table)

Category 1 2 3 4
Frequency 72 45 60 68

Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

2.

The quality department at an electronics company has noted that, historically, 94% of the units of a specific product pass a test operation, 4% fail the test but are able to be repaired, and 2% fail the test and need to be scrapped. Due to recent process improvements, the quality department would like to test if the rates have changed. A recent sample of 500 parts revealed that 478 parts passed the test, 16 parts failed the test but were repairable, and 6 parts failed the test and were scrapped. (You may find it useful to reference the appropriate table: chi-square table or F table)

Compute the value of the test statistic. (Round the intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Homework Answers

Answer #1

1) applying chi square test statistic:

           relative observed Expected residual Chi square
category frequency Oi Ei=total*p R2i=(Oi-Ei)/√Ei R2i=(Oi-Ei)2/Ei
1 0.250 72.000 61.25 1.37 1.887
2 0.250 45.000 61.25 -2.08 4.311
3 0.250 60 61.25 -0.16 0.026
4 0.250 68 61.25 0.86 0.744
total 1.000 245 245 6.967

value of the test statistic =6.967

2)

           relative observed Expected residual Chi square
category frequency Oi Ei=total*p R2i=(Oi-Ei)/√Ei R2i=(Oi-Ei)2/Ei
1 0.940 478.000 470.00 0.37 0.136
2 0.040 16.000 20.00 -0.89 0.800
3 0.020 6 10.00 -1.26 1.600
total 1.000 500 500 2.536

value of the test statistic =2.536

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