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# Hypothesis Testing, Confidence Interval&Binomial Probability

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1.A sample of 64 college students are asked their weekly (at school) expenses during the fall term. The enquire resulted in a mean of \$55 with a standard deviation of \$12. Construct a 95% confidence interval for the mean expense for all the students in the school.

a. Value from the table ____________
b. The confidence interval is (in interval form) _____________
c. The researcher is confident that only 5% of possible samples would have an estimation of error of __________________

2. In a large university, approximately 30% of the juniors are undecided with respect to their major. A sample of 20 junior students is selected at random. Assume a binomial distribution. Compute:

a. the expected number of undecided majors in the sample
b. The probability that more of 7 students in the sample are undecided major

3. A medicine manufacturer claims that for a new pain reliever it takes less than 15 minutes to relieve a common headache. He conducted a t-test of hypothesis by giving the new medicine to 10 patients suffer a common headache. The sample mean and standard deviation are respectfully 14.2 minutes and 2.1 minutes. Answer the following questions.

a. Write the Alternative Hypothesis
b. The critical value should be
c. The test statistics is
d. Do the data provide evidence to question the manufacture's claim?
e. When using this procedure you are assuming that the relieving time is approximately __________________ distributed.

4. According to a recent study, at least 25% of children are not leaving with their parents. In rural region of the county , in a random sample of 300 children, 57 were not lining with their parents. With alpha= 0.05 test the claim that in the region under percent of children not living with their parents is less than the national percent.

a. The alternative hypothesis is
b. The test statistics is
c. For alpha 0.05 the critical value is
d. The statistical decision should be
e. Do the dat provide to support the stated claim?
f. Find p-value

5. Determine, in the following situations, whether is a case for independent or dependent samples.

a. The effectiveness of some medicine to treat high blood pressure is tested by measuring the blood pressure in a group of patients treated with medicine and another group of patients that were given a placebo.

b. The effectiveness of some medicine to treat high blood pressure is tested by the blood pressure in a group of patients before and after the dug administration. The data consists of before and after measurements for each patient.