1.A study of North York University students showed the mean age of all students in the first year of university to be 20.3 years old with a standard deviation of 1.07 years. A randomly selected subgroup of these first-year students also averaged 20.1 years in age with a standard deviation 1.09 years.

a)Select any correct pair of label and value below:

• x=20.3ands=1.07

. x=20.3and=1.07

• =20.3ands=1.09
• =20.3and=1.09
• x=20.1ands=1.07
• x=20.1and=1.07
• =20.1ands=1.09
• =20.1and=1.07

2.The confidence interval for the population mean is often presented as

Lower Limit<

or

xME

(Sample MeanMargin of Error)

Use your knowledge of the confidence interval to determine the missing values for the 3 confidence intervals in the table below.

Report answers accurate to 2 (two) decimal places.

Sample MeanMarginof Error LowerLimit UpperLimit

Interval 1 169.32 162.16

Interval 2 4.43 161.54

Interval 3 111.43 7.45

3.For each confidence level in the table below, determine the right-tail area (/2) and the corresponding critical z-value (z_/2).

Report right-tail area as decimal (not percent) accurate to 4 decimal places.

Report (positive) critical values accurate to 2 decimal places.

Confidence Level Right Tail Area (/2) Critical Value (z_/2)

76.2%

82.3%

90.9%

The results show that the smaller the confidence level, theSelect an answer

smaller

larger

the tail area, and theSelect an answer

larger

smaller

the critical value.

4.In constructing a confidence interval for the population mean using thet-distribution, we often need the degrees of freedom (df), confidence level, and the critical value.

Use the Studentt-distribution to determine the missing values in the table below.

Report the positivetcritical value accurate to 3 decimal places.

Sample size Degrees of freedom Confidence level Criticalvalue (t)

9 % 1.860

16 95%

15 % 2.977

23 98%

5.

Ifn=13,x=37, ands=9, construct a confidence interval at a90%

confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

------<<-------

6.Suppose (10, 52) is a 95% confidence interval estimate for a population mean.

a) The point estimatex=

b) The margin of error =

c) Which of the following are true statements?

I. There is a 0.95 probability thatis between 10 and 52.

II. There's a 95% chance that any particular value in the population will fall between 10 and 52.

III. 95% of confidence intervals constructed in this population will have a lower limit of 10 and an upper limit of 52.

IV. If 95% confidence intervals are calculated from all possible samples of the given size,is expected to be in 95% of these intervals.

• IV only
• I and III
• I and IV
• II and III
• I and II
• III only

7.You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximate=49.4

. You would like to be 92% confident that your estimate is within 0.2 of the true population mean. How large of sample size is required?

Do not round mid-calculation. However, use acritical z value accurate to two (2) decimal places.

n=

8.The table below contains the birth weights in grams of 26 African American babies born at BayState Medical Center in Springfield, Massachusetts in 1986. Compute a 95% confidence interval for birth weight.

Directions:Click on the Data button below to display the data. Copy the data into a statistical software package and click the Data button a second time to hide it.

Weight

2528

2762

2885

2897

2939

2989

2977

3004

3047

3353

3383

3430

3478

3784

3831

1129

1685

1949

2131

2181

2331

2363

2373

2404

2440

2467

a)Find the point estimate for the birth weights. Round your answer to 2 decimal places.

b)Determine the value oftc. Round your answer to 5 decimal places.

c)Find the margin of error for the confidence interval. Round your answer to 1 decimal place.

d)Construct the confidence interval for birth weights. Enter your answer as an open interval of the form (a,b) and round to the nearest integer.

e)Babies weighing less than 2500 grams are considered to be of low birth weight. Can you conclude that the average birth weight is greater than 2500 grams?

• No, the entire confidence interval is below2500
• Yes, the entire confidence is above2500
• No conclusions can be drawn since the confidence interval contains2500