Question

In planning a study of birth weights of babies whose mothers did not see a doctor before delivery, a researcher states the hypotheses as

LaTeX: H_0: \bar{x} = 1000 grams \\H_a: \bar{x}<1000 grams H 0 : x ¯ = 1000 g r a m s H a : x ¯ < 1000 g r a m s

What is wrong with the hypotheses as they are written?

Group of answer choices

Nothing is wrong with the hypotheses.

Hypotheses are about the population mean of birth weights. Therefore the symbol should LaTeX: \mu μ be used instead of LaTeX: \bar{x} x ¯ .

Birth weight is categorical. Therefore the symbol used should be LaTeX: \hat{p} p ^ a instead of LaTeX: \bar{x} x ¯ .

The alternative hypothesis should contain the equal sign and the null should have the “less than” symbol.

Answer 1

the hypotheses as

We know that indicates the sample mean and indicates the population mean. Here, the researcher wants to study the birth weights of babies whose mothers did not see a doctor before delivery for the entire population. The researcher will be using a sample to make inference about the population of babies. Having collected a sample, the researcher knows the exact value of for that sample and hence there is no mystery there. However, what can the researcher infer about the based on this sample?

Hence the correct hypotheses are

ans: Hypotheses are about the population mean of birth weights. Therefore the symbol should μ be used instead of