1 . Determine the critical region and the critical values used to test the follo

Question

1. Determine the critical region and the critical values used to test the following null hypotheses. (Assume a Z-test statistic is appropriate here.)

(a) H0: = 57 (), Ha: < 57, = 0.01

(b) H0: = 75 (), Ha: < 75, = 0.02

(c) H0: = 100, Ha: 100, = 0.1

(d) H0: = 18.7 (), Ha: > 18.7, = 0.05

2. Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows.

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use = 0.10.

(a) What is the level of significance?


State the null and alternate hypotheses.

H0: = 4.64; H1:   < 4.64

H0: = 4.64; H1:   > 4.64     

H0: > 4.64; H1:   = 4.64

H0: < 4.64; H1:   = 4.64

H0: = 4.64; H1:   4.64

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

The Student's t, since we assume that x has a normal distribution and is unknown.The standard normal, since we assume that x has a normal distribution and is unknown.     The standard normal, since we assume that x has a normal distribution and is known.The Student's t, since we assume that x has a normal distribution and is known.

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


(c) Find the P-value. (Round your answer to four decimal places.)


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 ?

At the = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.At the = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.     At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

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

There is insufficient evidence at the 0.10 level to reject the claim that the population mean RBC count for the patient is not lower than 4.64.There is sufficient evidence at the 0.10 level to reject the claim that the population mean RBC count for the patient is not lower than 4.64.

3. Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of = 66 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm).

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(ii) Assume the slab thickness has an approximately normal distribution. Use a 5% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.

(a) What is the level of significance?


State the null and alternate hypotheses.

H0: = 66; H1:   66H0: = 66; H1:   < 66     H0: < 66; H1:   = 66H0: = 66; H1:   > 66H0: 66; H1:   = 66

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

The Student's t, since we assume that x has a normal distribution and is unknown.The Student's t, since we assume that x has a normal distribution and is known.     The standard normal, since we assume that x has a normal distribution and is unknown.The standard normal, since we assume that x has a normal distribution and is known.

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


(c) Find the P-value. (Round your answer to four decimal places.)


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 ?

At the = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.     At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the = 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 reject the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.There is insufficient evidence at the 0.05 level to reject the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.

Explanation / Answer

1. Determine the critical region and the critical values used to test the following null hypotheses. (Assume a Z-test statistic is appropriate here.)

(a) H0: = 57 (), Ha: < 57, = 0.01

1 tailed alpha = 0.01 critical value : -2.32

(b) H0: = 75 (), Ha: < 75, = 0.02

critical value : - 2.05

(c) H0: = 100, Ha: 100, = 0.1 alpha / 2 = 0.05

critical values : +/-1.64

(d) H0: = 18.7 (), Ha: > 18.7, = 0.05

critica values : 1.64

all critical values are from the table of normal distributon Z

for the other questions please post it in a new question

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