Question

For all hypothesis testing problems Find each steps. Traditional method Step

1 State the null, alternative hypothesis, and identify the claim Step

2 Find the critical region and critical value(s) Step

3: Compute the test value Step

4 Make the decision to reject or do not reject H0 and conclusion.

Show how you arrived at your solution on the answer sheet for full credit. Write neatly, clearly and be organized.

1.The average hemoglobin reading for a sample of 20 teachers was 16 grams per 100 milliliters, with a sample standard deviation of 2 grams per 100 milliliters. (15 points)

a) Find the 99% confidence interval of the true mean.

b) Support the medical research team is investigating that true mean is 19 grams per 100 milliliters in a previous year, does your sample suggest that the true population mean for all teacher should be reject? Explain

c) Support the medical research team is investigating that true mean is 14 grams per 100 milliliters in a previous year, does your sample suggest that the true population mean for all teacher should be reject?

Explain 2. Of 318 randomly selected medical students, 21 said that they planned to work in a rural community. (15 points)

a) Find a 90% confidence interval for the true proportion of all medical students who plan to work in a rural community. Write your answer with three decimal places

b) If the population proportion is 0.037. Do you reject the population proportion? Explain

c) If the population proportion is 0.083. Do you reject the population proportion? Explain 3.

The manager of a large factory believes that the average hourly wage of the employees is below $9.98 per hour. A sample of 18 employees has a mean $9.60. the sample standard deviation is $1.42. At α = 0.10, is there enough evidence to support the manager’s claim? Use Traditional method (10 points)

4. A travel associate claim that the mean daily meal cost for two adults traveling together on vacation in New York is $105. A random sample of 20 such groups of adults has a mean daily meal cost of $110 and a sample standard deviation of $8.50. Is there enough evidence to reject the claim at α = 0.05? Use Traditional method (10 points)

5. Researchers suspect that 18% of all high school students smoke at least one pack of cigarettes a day. In New York one high school, with an enrollment of 300 students, a study found that 50 students smoked at least one pack of cigarettes a day. At α = 0.02, can the study conclude that 18% of all high school students smoke at least one pack of cigarettes a day? Use Traditional method (10 points)

6. A humane society claim that 35% of U.S. households own a cat. In a random sample of 300 U.S. households, 24% say they own a cat. At α = 0.02, is there enough evidence to reject the society’s claim? Use Traditional method (10 points)

Answer 1

Solution:-

6)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.35
Alternative hypothesis: P 0.35

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.02. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.02754
z = (p - P) /S.D

z = - 3.99

z_critical = + 2.327

Rejection region is - 2.327 > z > 2.327.

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Interpret results. Since the z-value lies in the rejection region, hence we have to reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that that 35% of U.S. households own a cat.