Final answer:
Option d is correct: the chi-square test result indicates a probability between 50% and 90% that the difference between expected and observed progeny is due to chance, showing no significant deviation from the null hypothesis.
Step-by-step explanation:
In the context of a chi-square test, a calculated chi-square (X²) value of 0.375 with 1 degree of freedom that corresponds to a probability between 0.5 and 0.9 indicates that there is between a 50% and 90% chance that the difference between the expected and observed progeny in an experiment is due to chance. This result suggests that there is not a significant difference from what was expected based on the null hypothesis. Therefore, option d: 'There is between a 50% and 90% chance that the difference between expected and observed progeny is due to chance' is the correct interpretation of the chi-square test results.
The degree of freedom (df) is calculated as the number of categories minus one. In chi-square tests, particularly the goodness-of-fit test, the null hypothesis states that the observed data fit the expected distribution. If the observed and expected values are close, the test statistic is small and suggests that any difference might be due to random sampling variability rather than systemic differences.
It is also essential to ensure that each expected cell value is at least five to validly use the chi-square test. When performing a test with a significant level of 0.05 and finding a high p-value (between 0.5 and 0.9), as in this scenario, it generally means that there isn't strong enough evidence to reject the null hypothesis, implying that there is no significant difference between observed and expected data.