Question

Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution.

9.9 8.8 10.9 9.3 9.4 9.8 10.0 9.9 11.2 12.1

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x and the sample standard deviation s. (Round your answers to two decimal places.)

x = mg/dl

s = mg/dl

(b) Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (Round your answer to two decimal places.)

lower limit mg/dl

upper limit mg/dl

(c) Based on your results in part (b), do you think this patient still has a calcium deficiency? Explain.

Yes. This confidence interval suggests that the patient may still have a calcium deficiency.

Yes. This confidence interval suggests that the patient no longer has a calcium deficiency.

No. This confidence interval suggests that the patient may still have a calcium deficiency.

No. This confidence interval suggests that the patient no longer has a calcium deficiency.

Correct: Your answer is correct.

The following data represent crime rates per 1000 population for a random sample of 46 Denver neighborhoods.†

63.2 36.3 26.2 53.2 65.3 32.0 65.0

66.3 68.9 35.2 25.1 32.5 54.0 42.4

77.5 123.2 66.3 92.7 56.9 77.1 27.5

69.2 73.8 71.5 58.5 67.2 78.6 33.2

74.9 45.1 132.1 104.7 63.2 59.6 75.7

39.2 69.9 87.5 56.0 154.2 85.5 77.5

84.7 24.2 37.5 41.1

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.)

x = crimes per 1000 people

s = crimes per 1000 people

(b) Let us say the preceding data are representative of the population crime rates in Denver neighborhoods. Compute an 80% confidence interval for μ, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.)

lower limit crimes per 1000 people

upper limit crimes per 1000 people

(c) Suppose you are advising the police department about police patrol assignments. One neighborhood has a crime rate of 56 crimes per 1000 population. Do you think that this rate is below the average population crime rate and that fewer patrols could safely be assigned to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate is below the average population crime rate.

Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

No. The confidence interval indicates that this crime rate is below the average population crime rate.

No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

Correct: Your answer is correct.

(d) Another neighborhood has a crime rate of 76 crimes per 1000 population. Does this crime rate seem to be higher than the population average? Would you recommend assigning more patrols to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate.

No. The confidence interval indicates that this crime rate is higher than the average population crime rate.

No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

Correct: Your answer is correct.

(e) Compute a 95% confidence interval for μ, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.)

lower limit crimes per 1000 people

upper limit crimes per 1000 people

(f) Suppose you are advising the police department about police patrol assignments. One neighborhood has a crime rate of 56 crimes per 1000 population. Do you think that this rate is below the average population crime rate and that fewer patrols could safely be assigned to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate is below the average population crime rate.

Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

No. The confidence interval indicates that this crime rate is below the average population crime rate.

No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

Correct: Your answer is correct.

(g) Another neighborhood has a crime rate of 76 crimes per 1000 population. Does this crime rate seem to be higher than the population average? Would you recommend assigning more patrols to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate.

No. The confidence interval indicates that this crime rate is higher than the average population crime rate.

No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

Correct: Your answer is correct.

(h) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem.

Yes. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.

Yes. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.

No. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.

No. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.

Correct: Your answer is correct.

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The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8

2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4

3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9

1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0

1.2 1.8 2.4

(a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x = %

s = %

(b) Compute a 90% confidence interval for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.)

lower limit %

upper limit %

(c) Compute a 99% confidence interval for the population mean μ of home run percentages for all professional baseball players. (Round your answers to two decimal places.)

lower limit %

upper limit %

(d) The home run percentages for three professional players are below.

Player A, 2.5 Player B, 2.3 Player C, 3.8

Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.

We can say Player A falls close to the average, Player B is above average, and Player C is below average.

We can say Player A falls close to the average, Player B is below average, and Player C is above average.

We can say Player A and Player B fall close to the average, while Player C is above average.

We can say Player A and Player B fall close to the average, while Player C is below average.

Correct: Your answer is correct.

(e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem.

Yes. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.

Yes. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.

No. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.

No. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.

1 T-Mobile Wi-Fi 3:45 PM webassign.net 10. 0.2/1 points Previous Answers UnderStat127.2017. My Notes Ask Your Teacher Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution. 9. 9 8 10.9 49 10.0 11.2 12.1 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x and the sample standard deviation s. (Round your answers to two decimal places.) mg/d (b) Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (Round your answer to two decimal places.) upper limit (c) Based on your results in part (b), do you think this patient still has a calcium deficiency? Explain. Yes. This confidence interval suggests that the patient may still have a calcium deficiency. Yes. This confidence interval suggests that the patient no longer has a calcium deficiency. No. This confidence interval suggests that the patient may still have a calcium deficiency. o No. This confidence interval suggests that the patient no longer has a calcium deficiency. Need Help? 1/1 points Previous Answers BBUnderstat1272.019. My Notes Ask Your Teacher The distribution of heights of 18-year-old men in the United States is approximately normal, with mean 68 inches and standard deviation 3 inches (U.S. Census Bureau). In Minitab, we can simulate the drawing of random samples of size 20 from this population (Calc Random Data Normal, with 20 rows from a distribution with mean 68 and standard deviation 3). Then we can have Minitab compute a 95% confidence interval and draw a boxplot of the data ( Stat - Basic Statistics 1 -- Sample t, with boxplot selected in the graphs). The boxplots and confidence intervals for four different samples are shown in the accompanying figures. The four confidence intervals are as follows. Sumple 67.358 . 1 .12

Answer 1

1)

a)

Sample Mean,    x̅ = ΣX/n =    10.13
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   0.99

b)

Level of Significance ,    α =    0.001          
degree of freedom=   DF=n-1=   9          
't value='   tα/2=   4.7809   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   0.9911   / √   10   =   0.3134
margin of error , E=t*SE =   4.7809   *   0.3134   =   1.4984
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    10.13   -   1.498443   =   8.6316
Interval Upper Limit = x̅ + E =    10.13   -   1.498443   =   11.6284
99.9%   confidence interval is (   8.63   < µ <   11.63   )

c)

No. This confidence interval suggests that the patient no longer has a calcium deficiency.