1. State the claim mathematically.
Then write the null and alternative hypothesis.
Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
a. A research hospital claims that more than 3.7% of the population suffers from high
blood pressure. Use p, the represent the population proportion.
Answer:
Claim: p>0.037
H0 : p≤0.037
Ha : p>0.037
Test : z-test
b. The highest acceptable level of pesticide found in quail has been limited to 0.35 parts
per million (ppm). A hypothesis test is perform to test if the level of the pesticide is
higher.
Answer:
Claim: p>0.35
H0 : p≤0.35
Ha : p>0.35
Test : z-test
Hypothesis Testing for the Mean (Large Samples) Use the guidelines at the end of the
project.
2. Use the method specified to perform the hypothesis test for the population mean .
WeatherBug say that the mean daily high for December in a large Florida city is 76
degrees F. WFLA weather suspects that this temperature is not accurate. A hypothesis
test is performed the determine if the mean is actually lower than 76 degrees F.
Assume that the population standard deviation of = 5.6 F. A sample of mean daily
temperatures for December over the past 40 years gives x bar 74 degrees F. At a =
0.01, does the data provide sufficient evidence to conclude that the mean
temperature is lower than 76 degrees F.
a. Use the critical value z0 method from the normal distribution.
1.
H0 : u≥76
Ha : u<76
2. a = 0.01
3. Test statistics: z-test , z=-2.259
4. P-value or critical z0 or t0.; z0=-2.326
5. Rejection Region: {z/z<-2.326}
6. Decision: We don´t reject H0
7. Interpretation: there is no enough evidence to conclude that the mean temperature
is lower than 76 degrees F
b. Use the P-value method.
1.
H0 : u≥76
Ha : u<76
2. a = 0.01
3. Test statistics: z-test, z=-2.259
4. P-value or critical z0 or t0.; p-value =0.0119
5. Rejection Region: We reject H0 if the p-value < 0.01
6. Decision: we don´t reject H0
7. Interpretation: there is no enough evidence to conclude that the mean temperature
is lower than 76 degrees F
Hypothesis Testing for Mean (Small Samples)
3. A local tire store suspects that the mean life of a new discount tire is less that
39,000 miles. To check the claim, the store selects randomly 18 of these new discount
tires. When they are tested, it is found that the mean life is 38,250 miles with a sample
standard deviation s = 1200 miles. Assume the distribution is normally distributed. a.
Use the critical value t0 method from the normal distribution to test for the
population mean u. Test the company’s claim at the level of significance a = 0.05.
1. H0 : u=39,000
Ha : u<39,000
2. a = 0.05
3. Test statistics: t-test: df=17, t=-2.652
4. P-value or critical z0 or t0. ; t0=-1.74
5. Rejection Region: {t/t<-1.74}
6. Decision: Reject H0
7. Interpretation: there is enough evidence to suspect that the mean life of a new
discount tire is less that 39,000 miles.
b. Use the critical value t0 method from the normal distribution to test for the
population mean u. Test the company’s claim at the level of significance a = 0.01
1. H0 : u=39,000
Ha : u<39,000
2. a = 0.01
3. Test statistics: =-2.652
4. P-value or critical z0 or t0. T0=-2.567
5. Rejection Region: {t/t<-2.567}
6. Decision: Reject H0
7. Interpretation:
there is enough evidence to suspect that the mean life of a new discount tire is less
that 39,000 miles
Hypothesis Testing for Proportions.
4. A flash drive manufacturer has set a standard on their production process. When
defects exceed 3%, the production process is unacceptable. A random sample of 300
drives is tested. The defective rate is 5.9%. Use a level of significance of a = 0.01 to test
to see if you have sufficient evidence to support the claim that the defective rate
exceeds 3%. (Round phat to 3 decimal places.)
1. H0 : p=0.03
Ha : p>0.03
2. a = 0.01
3. Test statistics: z-test: z=2.945
4. P-value or critical z0 or t0. Zo=2.326
5. Rejection Region: {z/z>2.326}
6. Decision: we reject H0
7. Interpretation: there is sufficient evidence to support the claim that the defective
rate exceeds 3%.
Guidelines -- Hypothesis Testing Steps:
1. State H0 and Ha.
2. Specify the level of significance alpha ?.
3. Determine the test statistic, either z or t. Find the test statistic using the given data.
4. Find the P-value or the critical value(s) z0 or t0. Use the method specified in the
problem statement.
5. Define the rejection region using either the P-value method or critical values from
the Normal distribution.
6. Make a decision t