Question

1. A research company surveyed 650 adults in the US to estimate what percent of the country were afraid of their identity being stolen. From the sample, 408 indicated that they were afraid of their identity being stolen. Find the 92% confidence interval for the proportion of all adults in the US who are afraid of their identity being stolen. Round to 4 decimal points.

2. A laboratory tested 90 chicken eggs and found that the mean amount of cholesterol was 213.5 milligrams with a standard deviation of 19.0 milligrams. Construct a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs. round to 4 decimals

3. A random sample of 86 light bulbs had a mean life of 545 hours with a standard deviation of 29 hours. Construct a 90% confidence interval for the mean life, μ, of all light bulbs of this type. round to 4 decimals.

4. A government agency would like to know the average weight of adult catfish in the wild. The need to know how many fish to sample. The population standard deviation is known to be 16.8 lbs from previous studies.

(a) Assuming that they would like to be 90% confident of the results, what is the critical value that corresponds to this given level of confidence? Round to two decimals and remember that critical values are defined to be positive.

(b) If they would like to have a maximum error of 1.4 lbs, how many fish should be sampled?

5. The US government spent $4.5 billion (about $16 per resident) on the 2000 census. As a money savings device, statisticians have recommended the use of sampling techniques as opposed to polling the entire population. Based on the 2000 census, the population standard deviation of ages in the US is known to be 22.57 years.

(a) Assuming that we would like to be 99% confident of the results, what is the critical value that corresponds to this given level of confidence? Round to two decimals and remember that critical values are defined to be positive.

(b) If we would like to have a maximum error of 0.15 years, how many residents should be sampled?

6. A brochure claims that the average maximum height for a certain type of plant is 0.7 m. A gardener suspects that this is not accurate locally due to variation in soil conditions, and believes the local height is shorter. A random sample of 40 mature plants is taken. The mean height of the sample is 0.65 m with a standard deviation of 0.20 m. Test the claim that the local mean height is less than 0.7 m using a 5% level of significance.

a. Enter the Null Hypothesis for this test: H0:

b. Enter the Alternative Hypothesis for this test: H1:

c. Is the original claim in the Null Hypothesis (H0) or the Alternative Hypothesis (H1)? Answer using either H0 or H1.
d. What is the p-value for this hypothesis test? Round your answer to four decimal places.
e. What is the decision based on the given sample statistics?

f. What is the correct interpretation of the decision?

There

enough evidence to

the claim that the mean height of the plant locally is different from 0.7 m.

Answer 1