In order to find a 93% confidence interval we need to find values a and b such that for ZN(=0,=1),P(a

(a) Suppose a=2.3761.

Then b=

Answer

.

(b) Suppose b=2.0877.

Then a=

Answer .

Please answer all parts of the question.

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Question 2

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The blood pressure of a person changes throughout the day. Suppose the systolic blood pressure of a person is measured 29 times over several days and the standard deviation of these measurements for the person is known to be =9.9

mmHg. Let be the true average blood pressure for that person and let x=83

be the average of the 29 measurements.

(a) Find a two-sided 94% confidence interval for .

One can be 94% confident that the true average blood pressure

for that person is between Answer and Answer .

(b) Find a lower-bound 94% confidence interval for .

One can be 94% confident that the true average blood pressure

for that person is at least Answer .

(c) Find an upper-bound 94% confidence interval for .

One can be 94% confident that the true average blood pressure

for that person is at most Answer .

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You are interested in the weight gain of the Auburn Freshman. You think that the average weight gain of the Auburn Freshman student is not 15 pounds. You collect a random sample of measurements. The weight gains are (a negative value indicates a weight loss):

6, 16, 9, 19, 10, 11, 12, 14, 10

You may assume for the following questions that the distribution of weight gain is normal.

(a) State the appropriate hypothesis test. (This was done before collecting the data)

Null Hypothesis: Answer

Alternative Hypothesis:

Answer

(b) Calculate the sample mean x.x=

Answer

(c) Calculate the sample standard deviation s.

s=

Answer

(d) Evaluate the test statistic

T=x0s/n.T=

Answer

(e) The test statistic is t-distributed with Answer degrees of freedom.

(f) The p-value for the test is Answer.

(g) Should you reject the null hypothesis in favor of the alternative at significance level =0.01

?

Answer

(h) Is the weight gain significantly different from 15 lbs?

AnswerQuestion 4

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What is the life span of a lab mouse? You measured the following life spans (in days) for a certain standard inbred laboratory strain.

951, 568, 348, 738, 1125, 619, 812, 596, 577, 1317, 963, 651, 547, 707

You may assume for the following questions that the distribution of life span is normal.

(a) Calculate the sample mean x.

x=

Answer

(b) Calculate the sample standard deviation s.

s=

Answer

(c) Calculate the critical value t

for a 93 percent two-sided confidence interval. t=

Answer

(d) Calculate the margin of error m

for a two-sided confidence interval. m=

Answer

(e) The lower bound of the two-sided confidence interval is Answer and the upper bound of the two-sided confidence interval is Answer .

(f) Calculate the critical value t

for the 93 percent lower-bound confidence interval. t=

Answer

(g) Calculate the lower bound of the 93 percent lower-bound confidence interval. We can be 93 percent confident that the mean life span of the lab mouse is more than Answer days.

(h) Calculate the upper bound of the 93 percent upper-bound confidence interval. We can be 93 percent confident that the mean life span of the lab mouse is less than Answer days.

Please note that you must decide which of the three confidence intervals you wish to calculate before you look at the data. In particular, the confidence intervals in (g) and (h) are not simultaneously valid.