HW 4 - Hypothesis Testing -

Exercise 1

Lindsey thinks a certain potato chip maker is putting fewer chips in their regular bags of chips. From a random sample of 16 bags of potato chips she calculated a p-value of 0.076 for the sample.

  1. At a 5% level of significance, is there evidence that Lindsey is correct?
There is not enough evidence that Lindsey is correct, p-value > 0.05
  1. At a 10% level of significance, is there evidence that she is correct?
There is enough evidence that Lindsey is correct, p-value < 0.10

Exercise 2

In a statistical test of hypotheses, we say that the data are statistically significant at level \(\alpha\) if

  1. \(\alpha = 0.05\)
  2. \(\alpha\) is small
  3. the p value is larger than \(\alpha\)
  4. the p value is less than \(\alpha\)
d

Exercise 3

In formulating hypotheses for a statistical test of significance, the null hypothesis is often

  1. a statement that the data are all 0
  2. 0.05
  3. the probability of observing the data you actually obtained
  4. a statement of “no effect” or “no difference”
d

Exercise 4

According to the Merck Veterinary Manual, the average resting heart rate for a certain type of sheep dog is 115 beats per minute (bpm). A Montana farmer notices his aging sheep dog has been acting more lethargic than usual and wonders if her heart rate is slowing. He measures her heart rate on 15 occasions and finds a sample mean heart rate of 118.2 bpm.

Select the correct null hypothesis \(H_0\) and alternative hypothesis, \(H_a\)

\[ H_0 : \mu = 118.2 \\ H_a : \mu < 118.2 \]

\[ H_0 : \bar{x} = 118.2 \\ H_a : \bar{x} \neq 118.2 \]

\[ H_0 : \mu = 115 \\ H_a : \mu > 115 \]

\[ H_0 : \mu = 115 \\ H_a : \mu < 115 \]

c