In April 2025
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- In an obstetric hospital 17.8% of 320 women were delivered by forceps in 1980. What is the standard error of this percentage? In another hospital in the same region 22% of 185 women were delivered by forceps.
(a) What is the standard error of the difference between the percentage at this hospital and the first one? ( 8 marks)
(b) What is the 95% confidence interval of the differences between those two percentages?
(c) Was the difference in proportions statistically significant? ( 3 marks)
The following are data for 12 individuals’ daily sodium intake and their systolic blood pressure readings. A research investigator is interested in learning how strong the association is between these variables and how well we can predict blood pressure from sodium intake.
Person
1
2
3
4
5
6
7
8
9
10
11
12
Sodium (X)
6.8
7.0
6.9
7.2
7.3
7.0
7.0
7.5
7.3
7.1
6.5
6.4
BP (Y)
154
167
162
175
190
158
166
195
189
186
148
140
a. Calculate the correlation coefficient r and test if it is statistical significant at α = 0.05 level (5 marks)
b. Calculate the regression equation for data (10 marks)
c. What would be a likely blood pressure for a person with a sodium intake of:
i. 6.3 (2.5 marks)
ii. 7.6 (2.5 marks)
The value of serum sodium in healthy adults approximately follows a normal distribution with a mean of 141meq/l and standard deviation of 3meq/l
(a) What is the probability that a normal healthy adult will have a serum sodium value above 147meq/l ( 5 marks)
(b) What is the probability that a normal healthy adult will have a serum sodium value below 130 meq/l ( 5 marks)
(c) What is the probability that a normal healthy adult will have a serum sodium value between 132 and 150meq/l (5 marks)
In an obstetric hospital 17.8% of 320 women were delivered by forceps in 1980. What is the standard error of this percentage? In another hospital in the same region 22% of 185 women were delivered by forceps. (a) What is the standard error of the difference between the percentage at this hospital and the first one? ( 8 marks) (b) What is the 95% confidence interval of the differences between those two percentages? (4 marks) (c) Was the difference in proportions statistically significant? ( 3 marks)
Two cards are drawn at random from a set of 52 cards.What is the probability that the both cards are either kings or queens
'Bhartdarshan’ is an Internet-based travel agency wherein customers can see videos of the
cities they plan to visit. The number of hits daily is a normally distributed random variable
with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits?
Let X be a discrete random variable with the following PMF: pX(x) = 1/2 for x = 0 1/3 for x = 1 1/6 for x = 2 0 otherwise (i) Compute SX, the range of the random variable X. (ii) Calculate P(X ≤ 0.5). (iii) Calculate P(0.25 < X < 0.75). (iv) Calculate P(X = 0.2|X < 0.6).
a random sample of size n 16 is drawn from a normally distributed population. the sample mean is 98 with known standard deviation of 5. Construct a 98% confidence interval for the population mean.
Directions: Read the given situation, then state the possible consequence of an error made.
A quality control expert wants to test the null hypothesis that an imported solar panel is an effective source of energy.
2. Identify the Type II error in this context? What would be the possible consequence of committing the Type II error in this context?
a. They do not conclude that the solar panel is effective when it is not actually effective.
b. They do not conclude that the solar panel is effective when it is actually effective.
c. They conclude that the solar panel is effective when it is actually effective.
d. They conclude that the solar panel is effective when it is not actually effective.
Directions: Read the given situation, then state the possible consequence of an error made.
A quality control expert wants to test the null hypothesis that an imported solar panel is an effective source of energy.
1. Identify the Type I error in this context? What would be the possible consequence of committing the Type I error in this context?
a. They do not conclude that the solar panel is effective when it is not actually effective.
b. They do not conclude that the solar panel is effective when it is actually effective.
c. They conclude that the solar panel is effective when it is actually effective.
d. They conclude that the solar panel is effective when it is not actually effective.
