Question

an investigator wants to determine if a new program aimed at reducing the overall number of pregnancies in a highly populated area is effective (reducing average births below 6 per household). In order to carry out the investigation, the investigator surveys 20 participants in the program and finds the average number of births is 4.7 with a sample standard deviation of 0.9 births. carry out a test of hypothesis to test the investigator’s claim by answering the following with alpha=.01

research hypothesis:

Ha:

H0:

Test Statistic:

P-Value:

Conclusion in terms of the problem:

Possible error in terms of the problem:

B. Construct a 95% confidence interval for the average number of births per household in this study. Provide a correct interpretation of interval.

C. How many women should be sampled to estimate the actual average number of births within 1 person and a 96% confidence?

Answer 1

A)Research Hypothesis: We want to test whether a new program aimed at reducing the overall number of pregnancies in a highly populated area is effective (reducing average births below 6 per household).

The hypotheses are

Given the sample size and sample mean , sample standard deviation .

Since the population standard deviation is not known we use t-distribution.

The test statistic is

The P-value is

Since , we reject the null hypothesis.

We are 99% confident that the new program aimed at reducing the overall number of pregnancies in a highly populated area is effective (reducing average births below 6 per household).

We might have made a Type 2 error.

The two sided confidence interval for mean based on the sample data is

B)The 95% confidence interval is

C)We need

At least women should be sampled to estimate the actual average number of births within 1 person and a 96% confidence.