Question

An environmentalist collects a liter of water from 41 different locations along the banks of stream. He measures the amount of dissolved oxygen in each specimen. The sample mean oxygen level is 4.62 mg, with the sample standard deviation of 0.92. A water purifying company claims that the mean level of oxygen in the water is 5 mg. A hypothesis test with α = 1% is conducted to determine whether the mean oxygen level is less than 5 mg. 23. State the null and alternate hypotheses. 24. What is the level of significance? 25. What is the test statistic? Between what two values does the test statistic fall in between? 26. Between what two percentages do the P-value fall in between? 27. State your conclusion based on the P-value. For questions 28 to 32 , consider the following: The NCHS reported that the mean total cholesterol level for all adults was μ = 203 with σ = 36.3. From a random sample of n =300 patients, the sample mean was x̄ =200.3. Is there statistical evidence of a difference in mean cholesterol levels at α = 1%? 28. State the null and alternate hypotheses. 29. What is the level of significance? 30. What is the test statistic? 31. What is the P-value? 32. State your conclusion based on the P-value.

Answer 1

23)

  

24) The level of significance is 0.01

25) The test statistic is

  

26) df = 41 - 1 = 40

P-value = P(T < -2.645)

= 0.0058

0.005 < P-value < 0.01

Since the P-value is less than the significance level (0.0058 < 0.01), so we should reject the null hypothesis.

At 0.01 level of significance, there is not sufficient evidence to support the claim that the mean level of oxygen in the water is 5 mg.

28)

29) The level of significance is 0.01.

30) The test statistic is

  

31) P-value = 2 * P(Z < -1.29)

= 2 * 0.0985 = 0.1970

Since the P-value is greater than the significance level, so we should not reject the null hypothesis.

At 0.01 significance level, there is not sufficient evidence to conclude that there is a difference in the mean cholesterol level for adults.