Question

1)

The body weight of a healthy 3-month-old colt should be about μ = 62 kg.

(a) If you want to set up a statistical test to challenge the claim that μ = 62 kg, what would you use for the null hypothesis

H₀?

μ > 62 kgμ < 62 kg    μ = 62 kgμ ≠ 62 kg

(b) In Nevada, there are many herds of wild horses. Suppose you want to test the claim that the average weight of a wild Nevada colt (3 months old) is less than 62 kg. What would you use for the alternate hypothesis

H₁?

μ > 62 kgμ < 62 kg    μ = 62 kgμ ≠ 62 kg

(c) Suppose you want to test the claim that the average weight of such a wild colt is greater than 62 kg. What would you use for the alternate hypothesis?

μ > 62 kgμ < 62 kg    μ = 62 kgμ ≠ 62 kg

(d) Suppose you want to test the claim that the average weight of such a wild colt is different from 62 kg. What would you use for the alternate hypothesis?

μ > 62 kgμ < 62 kg    μ = 62 kgμ ≠ 62 kg

(e) For each of the tests in parts (b), (c), and (d), respectively, would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean?

both; left; rightleft; right; both    left; both; rightright; left; both

2)

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.8 with sample standard deviation s = 3.3. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 7.4; H₁: μ ≠ 7.4

H₀: μ = 7.4; H₁: μ > 7.4    

H₀: μ ≠ 7.4; H₁: μ = 7.4

H₀: μ > 7.4; H₁: μ = 7.4

H₀: μ = 7.4; H₁: μ < 7.4

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known.    The standard normal, since the sample size is large and σ is unknown.The Student's t, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250    0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.

Answer 1

(a)

(b)

(c)

(d)

(e)

left; right; both

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(a)

Level of significance = 5%

H₀: μ = 7.4; H₁: μ ≠ 7.4

(b)

The Student's t, since the sample size is large and σ is unknown.

(c)

Using t table the p-value is

0.010 < P-value < 0.050

(d)

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

(e)

There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.