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Chapter 3: Problem 17

The basis for rejecting any null hypothesis is arbitrary. The researcher can set more or less stringent standards by deciding to raise or lower the critical \(p\) value. Would the use of a standard of \(p=0.10\) be more or less stringent in failing to reject the null hypothesis? Explain.

Short Answer

Expert verified
Answer: Using a critical p-value of 0.10 would be less stringent than using lower critical p-values like 0.05 or 0.01. This means that there is a higher chance of committing a Type I error (falsely rejecting the null hypothesis) as we're allowing for weaker evidence against the null hypothesis.

Step by step solution

01

Understanding the Null Hypothesis and p-Values

The null hypothesis (\(H_0\)) is a statement that there is no significant difference, relationship, or effect between variables under investigation. The p-value is a probability value used to decide whether there is enough evidence to reject the null hypothesis. A smaller p-value indicates stronger evidence against the null hypothesis, and a larger p-value indicates weaker evidence against the null hypothesis.
02

Critical p-Values and Stringency

The critical p-value is a predetermined threshold below which we reject the null hypothesis. Common critical p-values are \(p=0.05\) or \(p=0.01\). The lower the critical p-value, the more stringent the criteria for rejecting the null hypothesis, meaning that there's a smaller chance of falsely rejecting the null hypothesis (Type I error).
03

Impact of Using a p-value of 0.10

Using a critical p-value of \(p=0.10\) would be less stringent than using \(p=0.05\) or \(p=0.01\). It allows for a higher probability of making a Type I error, which means falsely rejecting the null hypothesis when it is actually true. By using a p-value of 0.10, we would be more likely to reject the null hypothesis even when there isn't a significant difference, relationship, or effect.
04

Conclusion

The use of a standard of \(p=0.10\) would be less stringent in failing to reject the null hypothesis compared to using a lower critical p-value such as \(p=0.05\) or \(p=0.01\). It means that there is a higher chance of committing a Type I error (falsely rejecting the null hypothesis), as we're allowing for weaker evidence against the null hypothesis.

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Most popular questions from this chapter

In a cross between a black and a white guinea pig, all members of the \(F_{1}\) generation are black. The \(F_{2}\) generation is made up of approximately $3 / 4\( black and \)1 / 4$ white guinea pigs. Diagram this cross, and show the genotypes and phenotypes.

Two true-breeding pea plants are crossed. One parent is round, terminal, violet, constricted, while the other expresses the contrasting phenotypes of wrinkled, axial, white, full. The four pairs of contrasting traits are controlled by four genes, each located on a separate chromosome. In the \(F_{1}\) generation, only round, axial, violet, and full are expressed. In the \(\mathrm{F}_{2}\) generation, all possible combinations of these traits are expressed in ratios consistent with Mendelian inheritance. (a) What conclusion can you draw about the inheritance of these traits based on the \(\mathrm{F}_{1}\) results? (b) Which phenotype appears most frequently in the \(\mathrm{F}_{2}\) results? Write a mathematical expression that predicts the frequency of occurrence of this phenotype. (c) Which \(\mathrm{F}_{2}\) phenotype is expected to occur least frequently? Write a mathematical expression that predicts this frequency. (d) How often is either \(P_{1}\), phenotype likely to occur in the \(F_{2}\) generation? (e) If the \(F_{1}\) plant is testcrossed, how many different phenotypes will be produced?

Correlate Mendel's four postulates with what is now known about homologous chromosomes, genes, alleles, and the process of meiosis.

Distinguish between homozygosity and heterozygosity.

Mendel crossed peas with round, green seeds with peas having wrinkled, yellow seeds. All \(\mathrm{F}_{1}\) plants had seeds that were round and yellow. Predict the results of testcrossing these \(F_{1}\) plants.
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