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Histogram of Participants Switching their choice

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The histogram below indicates those who swapped boxers or wrestlers.
Calculation of the number of participants who decide to turn and who decide to sit
From the results, the following table was obtained from those who switched and those who remained.
MHD_answer
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
7
2.3
2.3
2.3
stay
179
60.1
60.1
62.4
switch
112
37.6
37.6
100.0
Total
298
100.0
100.0
From the data, 60% decided to stay while 38% switched while 2% did not indicate their options.
From the Chi-square, the following was achieved,
MHD_answer * MHD_type Crosstabulation
Count
MHD_type
Total
boxers
wrestlers
MHD_answer
5
2
7participants were more likely to switch their choice when presented with boxers’ scenario, the results indicate that the p value was over 0.005 indicating that the hypothesis was not be accepted (we reject the hypothesis). It can therefore be argued that participants with boxers’ scenario were not more likely to switch.

3. Number of participants that decide to switch and the number deciding to stay in response to the MHD depending
From running the analysis the following were arrived,

Unrevealed_initial_chance * MHD_answer Crosstabulation
Count
MHD_answer Total
stay switch
Unrevealed_initial_chance 20% 2 74 28 104
25% 2 54 44 100
30% 3 51 40 94
Total 7 179 112 298

Chi-Square Tests
Value df Asymp. Sig. (2-sided)
Pearson Chi-Square 8.544a 4 .074
Likelihood Ratio 8.708 4 .069
N of Valid Cases 298
a. 3 cells (33.3%) have expected count less than 5. The minimum expected count is 2.21.

From the data, it was evident that the p values of the data were above 0.05 and thus they were not significant. The hypothesis 2a indicates that participants would more likely switch to when they have a probability of 0.30 than when with a probability of 0.25. The results were not significant and thus the hypothesis was rejected.

4. Number of participants who decided to switch and who decided to stay on MHD depending on whether they were 25% or 20% unopened.
The following was the table based on those who decided to switch and those who decided to stay

Unrevealed_initial_chance * MHD_answer Crosstabulation
Count
MHD_answer Total
stay switch
Unrevealed_initial_chance 20% 2 74 28 104
25% 2 54 44 100
30% 3 51 40 94
Total 7 179 112 298
The Chi-square results were as follows;

Chi-Square Tests
Value df Asymp. Sig. (2-sided)
Pearson Chi-Square 8.544a 4 .074
Likelihood Ratio 8.708 4 .069
N of Valid Cases 298
a. 3 cells (33.3%) have expected count less than 5. The minimum expected count is 2.21.
Based on hypothesis 2b, the hypothesis in 2a indicates that participants would more likely switch to when they have a probability of 0.25 than when with a probability of 0.20, the p values were above 0.05 and thus they were not significant. The hypothesis should be rejected.

5. Mean and standard deviation of subjective numeracy scores for participants
The following were the mean and standard deviation of the above scores;
Statistics
Subjective_numeracy
N Valid 298
Missing 0
Mean 4.2504
Std. Error of Mean .04082
Median 4.3125
Mode 4.13
Std. Deviation .70468
Variance .497
Range 4.25

The LSD of 0.168, against an LSD of 0.704, then the hypothesis 3a is not supported.

6. Mean and Standard deviation of objective numeracy scores
From the data, the table was arrived,

Statistics
Objective_numeracy
N Valid 254
Missing 44
Mean 9.29
Std. Error of Mean .108
Median 10.00
Mode 11
Std. Deviation 1.729
Variance 2.990
Range 9
Sum 2360
The LSD of 0.438 was valued against the calculated LSD of 1.729, and thus the hypothesis is not supported.

7. Present the scatterplot for subjective numeracy scores and objective numeracy scores
The table below was achieved after analyzing the data in terms of correlation between the subjective and objective numeracy scores.

Correlations
Subjective_numeracy Objective_numeracy
Subjective_numeracy Pearson Correlation 1 .210**
Sig. (2-tailed) .001
N 298 254
Objective_numeracy Pearson Correlation .210** 1
Sig. (2-tailed) .001
N 254 254
**. Correlation is significant at the 0.01 level (2-tailed).
The results indicated that the correlation was significant at 0.01.
The results support the conclusions earlier made on hypothesis 3a and 3b.

8. How the collected data would limit drawing of the conclusions
The errors presented during data collection, errors presented during analyzing and errors presented during data presentation could hamper the way conclusions were made. The issues of errors could affect the extent to which they present true data (Wheelan, 2013)

References
Wheelan, C. (2013). The Monty Hall Problem. In C. Wheelan, Naked Statistics: Stripping the dread from data (pp 90-94). New York: W. W. Norton & Company.

October 20, 2021
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