Question

In: Statistics and Probability

Apply the χ2 goodness‐of‐fit test to the data in column 1 and test the assumption of...

Apply the χ² goodness‐of‐fit test to the data in column 1 and test the assumption of a normal distribution.

Measured Force Data for Exercise Problems

F (N) Set 1	F (N) Set 2	F (N) Set 3
51.9	51.9	51.1
51.0	48.7	50.1
50.3	51.1	51.4
49.6	51.7	50.5
51.0	49.9	49.7
50.0	48.8	51.6
48.9	52.5	51.0
50.5	51.7	49.5
50.9	51.3	52.4
52.4	52.6	49.5
51.3	49.4	51.6
50.7	50.3	49.4
52.0	50.3	50.8
49.4	50.2	50.8
49.7	50.9	50.2
50.5	52.1	50.1
50.7	49.3	52.3
49.4	50.7	48.9
49.9	50.5	50.4
49.2	49.7	51.5

Expert Solution

The Chi-Square goodness of fit test to test whether the normality assumption is true for column 1 is performed in following steps in excel.

Step 1: Write the data value in excel. The screenshot is shown below,

Step 2: The mean and standard deviation for the data values are obtained using the excel functions =AVERAGE() and STDEV(). The screenshot is shown below,

Step 3: The Z score for each data values are obtained using the formula,

The screenshot is shown below,

Step 4: The observed value are obtained by counting the Z score as follows,

The observed values are,

Observed values
Z score	Count
Z<-1	4
-1<Z<0	5
0<Z<1	8
Z>1	3

Step 5: The expected values are obtained in excel. The screenshot is shown below,

The expected values are,

Expected values
Z score	Count
Z<-1	3.173
-1<Z<0	6.827
0<Z<1	6.827
Z>1	3.173

Step 6: The Chi-Square statistic is obtained using the formula,

Z score	Observed,	Expected,
Z<-1	4	3.173	0.827	0.684	0.215
-1<Z<0	5	6.827	-1.827	3.338	0.489
0<Z<1	8	6.827	1.173	1.376	0.202
Z>1	3	3.173	-0.173	0.030	0.009
				Sum	0.915

Step 7: The P-value for the chi square is obtained for chi square = 0.915 and degree of freedom = k - 1 = 4 - 1 = 3 using the excel function =1-CHISQ.DIST(0.915,3,TRUE)

Conclusion:

at 5% significance level. it can be concluded that the null hypothesis is not rejected. Hence we can conclude that the data values are normally distributed.

orchestra answered 2 years ago

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