# Hypothesis testing for blood plasma

Please provide the following information for the following 3 problems:

a) What is the level of significance? State the null and alternate hypothesis.

b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. What is the value of the sample test statistics?

c) Find the p value.

d) Based on answer from a & c, will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?

e) State your conclusion in the context of the application.

4) Medical Blood Plasma. Let x be the variable that represents the pH of the arterial plasma (i.e. acidity of the blood). For healthy adults, the mean of the x distribution is = 7.4. A new drug for arthritis has been developed.

Medical Blood Plasma. Let x be the variable that represents the pH of the arterial plasma (i.e. acidity of the blood). For healthy adults, the mean of the x distribution is = 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 too the drug for 3 months. Blood tests show the average pH to be xbar = 8.1 with a sample standard deviation s = 1.9. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of blood.

6) Fishing Trout. Pyramid Lake is on the Paiute Indian Reservation in the Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid lake is = 19 inches. However the creel survey reported that for a random sample of 51 fish caught, the mean length was xbar = 18.5 inches with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of a trout caught in Lake Pyramid is less than 19 inches? Use = 0.05.

14) Shopping time: House wares. How much customers buy is a direct result of how much time they spend in a store. The mean shopping time for women accompanied by children in national house wares stores is 7.3 minutes. A retail research team is studying shopping habits in the cherry creek mall (Denver). A random sample of women shoppers with children in a large house ware store gave the following shopping times (in minutes):

7.7 8.1 8.2 9.0 5.8 9.3 8.4 6.9 12.1 9.4

8.1 6.2 7.3 7.9 8.2 8.5 7.2 6.3 9.1 8.8

i) Use a calculator with the mean and the standard deviation keys to verify that xbar 8.1 min and s 1.4 min.

ii) Assume shopping time follows an approximately normal distribution. Use a 5% level of significance to test the claim that the average shopping time for women with children in the cherry creek mall is higher than the national average for this type of store.

#### Solution Preview

Please provide the following information for the following 3 problems:

4) Medical Blood Plasma. Let x be the variable that represents the pH of the arterial plasma (i.e. acidity of the blood). For healthy adults, the mean of the x distribution is = 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 too the drug for 3 months. Blood tests show the average pH to be xbar = 8.1 with a sample standard deviation s = 1.9. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of blood.

a) what is the level of significance? State the null and alternate hypothesis.

level of significance is 0.05.

H0:

H1:

b) what sampling distribution will you use? Explain the rationale for your choice of sampling distribution. What is the value of the sample test statistics?

Since the sample size is 31, we can apply central limit theorem and assume the sample mean is approximately normally distributed.

Value of test statistic =2.0513

c) find the p value

P-value = P( |Z|>2.0513)=2P(Z<-2.0513)=0.0404

d)based on answer from a & c, will you reject or fail to reject the null hypothesis? Are the data ...

#### Solution Summary

Hypothesis testing and the level of significance is examined.