Statistics and Probability Answers

A die was thrown twice. Find the probability of getting a 3 or 6.

From 50 life samples of mini drill bits made of low-carbon alloy steel, (expressed in the number of holes that can be drilled before it breaks), an average of 12.68 can be calculated, with a standard deviation of 6.83. Calculate a 95% confidence interval for the average mini drill in this condition.

One step in producing a spare part, involves drilling 4 holes. From 150 samples, the average time needed for this process is 72 seconds and SD = 10 seconds.
(a) calculate the CIs each with 95% CIs and 99.5% for the average time needed for the process.
(b) How many samples must be taken to get a 99.5% CI for averages in Ŧ 1.5 seconds from the actual price?

How can I make my statistical data on Ms word? And if the relation is indirect then how regression line touches to Y-axis?

QUESTIONS 9 TO 11 ARE BASED ON THE FOLLOWING INFORMATION.

A practicing statistician wants to test the following hypothesis at a 5% level of significance:

H0 : π = 0.25
H1 : π ≠ 0.25

From a sample of 100, p = 0.22

Question 9

What is the value of the test statistic?

(1) 0.72
(2) 0.72
(3) 0.69
(4) 0.69
(5) 1.44

Question 10

What is the p-value of the test?

(1) 0.4906
(2) 0.4716
(3) 0.2451
(4) 0.2358
(5) p-value < 0.002

Question 11

Consider the following decisions and reasons with regard to the practicing Statistician’s hypothesis test.

(A) Reject the null hypothesis because p-value < a
(B) Reject the null hypothesis because |Z| > |Za/2|
(C) Do not reject the null hypothesis because p-value > a.
(D) Do not reject the null hypothesis because |Z| < |Za/2|

Which of the above statements are correct?

(1) A only.
(2) C Only.
(3) A and B only.
(4) C and D only.
(5) A, B and C only.

Suppose we take a sample of 200 Facebook profiles and found only 34 to be ghost profiles. Use this information to answer questions 7 and 8.

Question 7

What is the 95% CI for the proportion of Facebook ghost profile?

(1) (0.1263; 0.2137)
(2) (0.1169; 0.2231)
(3) (0.1015; 0.2385)
(4) (0.1263; 0.2137)
(5) None of the above.


Question 8

What is the upper limit for the 99% confidence interval estimate of the proportion of Facebook ghost profiles?

(1) 0.2137
(2) 0.1015
(3) 0.2137
(4) 0.2385
(5) 0.2231

Question 5

Which of the following statements is incorrect?

(1) When only the sample size increases the CI estimate becomes narrower.
(2) When only the sample size decreases the CI estimate becomes wider.
(3) When only the confidence level increases the CI estimate becomes wider.
(4) When only the confidence level decreases the CI estimate becomes narrower.
(5) None of the above.

Question 6

The following intervals are the 90%, 95% and the 99% CI estimates for the population mean (in no
particular order):

(A) (196.06; 203.94)
(B) (194.82; 205.18)
(C) (196.70; 203.30)

Match the CI estimates to the appropriate CI level.

(1) A (90%), B (95%) and C (99%).
(2) A (95%), B (90%) and C (99%).
(3) A (99%), B (95%) and C (90%).
(4) A (90%), B (95%) and C (99%).
(5) A (95%), B (99%) and C (90%).

QUESTIONS 3 AND 4 ARE BASED ON THE FOLLOWING INFORMATION.

The number of times the AI algorithm is successful at detecting fake news is normally distributed
with a sample mean of 900 and the sample standard deviation of 30. Assume a sample size of
100 was used.

Question 3

What is the 95% confidence interval (CI) estimate for the population mean?

(1) (862.6636; 937.3364)
(2) (864.2155; 935.7845)
(3) (852.8959; 947.1041)
(4) (869.9665; 930.0335)
(5) None of the above.

Question 4

What is the 99% confidence interval estimate for the population mean?

(1) (862.6636; 937.3364)
(2) (864.2155; 935.7845)
(3) (852.8959; 947.1041)
(4) (869.9665; 930.0335)
(5) None of the above

Africa Check is interested in the activity of fake news tweets. From a sample of 50 tweets, there
are 100 impressions on average. Assume fake news tweet activity is normally distributed and the
population standard deviation is 25 impressions. Use this information to answer questions 1
and 2.

Question 1

What is the 90% confidence interval estimate for the population mean?

(1) (94.1840; 105.8160)
(2) (93.0704; 106.9296)
(3) (90.8783; 109.1217)
(4) (94.0709; 105.9291)
(5) None of the above.

Question 2

Suppose the sample size increases to 100 (while the mean and standard deviation remain the
same). What is the 90% confidence interval estimate for the population mean?

(1) (94.1840; 105.8160)
(2) (93.0704; 106.9296)
(3) (90.8783; 109.1217)
(4) (95.8875; 104.1125)
(5) (95.8075; 104.1925)

From past knowledge A Check knows that the true proportion of ghost profiles on Facebook is 0.2. Suppose we take a sample of 200 Facebook profiles and found only 34 to be ghost profiles. Use this information to answer questions 23 to 25.

Question 23

What is the value of the population proportion and sample proportion?

(1) π = 0.2 and p = 0.34
(2) π = 0.34 and p = 0.2
(3) π = 0.17 and p = 0.2
(4) π = 0.2 and p = 0.17
(5) π = 0.34 and p = 0.17

Question 24

Keeping in mind that the true proportion is known, what is the value of the standard error of the
proportion?

(1) 0.0283
(2) 0.0008
(3) 0.0335
(4) 0.0266
(5) None of the above.

Question 25

P(p ≥ 0.17) =?

(1) 0.8554
(2) 0.5120
(3) 0.4880
(4) 0.1446
(5) None of the above.