Name and Surname: CYPRUS INTERNATIONAL UNIVERSITY DEPARTMENT OF BASIC SCIENCES & HUMANITIES FACULTY of ARTS & SCIENCES STAT102-BIOSTATISTICS-II SPRING 2021-2022 MIDTERM EXAM Instructor(s): Asst. Prof. Dr Zalihe YARKINER 12.04.2022-60 MINUTES Q1.Suppose a researcher, interested in obtaining an estimate of the average level of some enzyme in a certain human population, takes a sample of 10 individuals, determines the level of the enzyme in each, and computes a sample mean of bar (x)=22 Suppose further it is known that the variable of interest is for population mean mu . approximately normally distributed with a variance of 45. We wish to estimate 95% interval a) 17.20leqslant mu leqslant 26.80 b) 17.74leqslant mu leqslant 25.16 c) 17.54leqslant mu leqslant 27.16 d) 17.84leqslant mu leqslant 26.16 Student No: Q2. The Pew Internet and American Life Project reported in 2003 that 18 percent of Internet users have used it to search for information regarding experimental treatments or medicines. The sample consisted of 1220 adult Internet users, and information was collected from telephone interviews.We wish to construct a 95 percent confidence interval for the proportion of Internet users in the sampled population who have searched for information on experimental treatments or medicines. a) 0.158leqslant pleqslant 0.202 b) 0.148leqslant pleqslant 0.102 c) 0.168leqslant pleqslant 0.212 d) 0.178leqslant pleqslant 0.232 Q3. Diskin et al.studied common breath metabolites such as ammonia, acetone,isoprene, ethanol, and acetaldehyde in five subjects over a period of 30 days. Each day breath samples were taken and analyzed in the early morning on arrival at the laboratory. For subject A, a 27-year-old female the ammonia concentration in parts per billion (ppb) followed a normal distribution over 30 days with mean 491 and standard deviation 119. What is the probability that on a random day, the subject'; ammonia concentration is between 292 and 649 ppb? a) 0.0475 b) 0.9082 c) 0.34 d) 0.8607 Q4. The statement "If there is sufficient evidence to reject a null hypothesis at the 10% significance level, then there is sufficient evidence to reject it at the 5% level" is: Please select the best answer of those provided below. a) Always True b) Never True c) Sometimes True; the p-value for the statistical test needs to be provided for a conclusion d) Not Enough Information;this would depend on the type of statistical test used

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Name and Surname: CYPRUS INTERNATIONAL UNIVERSITY DEPARTMENT OF BASIC SCIENCES & HUMANITIES FACULTY of ARTS & SCIENCES STAT102-BIOSTATISTICS-II SPRING 2021-2022 MIDTERM EXAM Instructor(s): Asst. Prof. Dr Zalihe YARKINER 12.04.2022-60 MINUTES Q1.Suppose a researcher, interested in obtaining an estimate of the average level of some enzyme in a certain human population, takes a sample of 10 individuals, determines the level of the enzyme in each, and computes a sample mean of bar (x)=22 Suppose further it is known that the variable of interest is for population mean mu . approximately normally distributed with a variance of 45. We wish to estimate 95% interval a) 17.20leqslant mu leqslant 26.80 b) 17.74leqslant mu leqslant 25.16 c) 17.54leqslant mu leqslant 27.16 d) 17.84leqslant mu leqslant 26.16 Student No: Q2. The Pew Internet and American Life Project reported in 2003 that 18 percent of Internet users have used it to search for information regarding experimental treatments or medicines. The sample consisted of 1220 adult Internet users, and information was collected from telephone interviews.We wish to construct a 95 percent confidence interval for the proportion of Internet users in the sampled population who have searched for information on experimental treatments or medicines. a) 0.158leqslant pleqslant 0.202 b) 0.148leqslant pleqslant 0.102 c) 0.168leqslant pleqslant 0.212 d) 0.178leqslant pleqslant 0.232 Q3. Diskin et al.studied common breath metabolites such as ammonia, acetone,isoprene, ethanol, and acetaldehyde in five subjects over a period of 30 days. Each day breath samples were taken and analyzed in the early morning on arrival at the laboratory. For subject A, a 27-year-old female the ammonia concentration in parts per billion (ppb) followed a normal distribution over 30 days with mean 491 and standard deviation 119. What is the probability that on a random day, the subject'; ammonia concentration is between 292 and 649 ppb? a) 0.0475 b) 0.9082 c) 0.34 d) 0.8607 Q4. The statement "If there is sufficient evidence to reject a null hypothesis at the 10% significance level, then there is sufficient evidence to reject it at the 5% level" is: Please select the best answer of those provided below. a) Always True b) Never True c) Sometimes True; the p-value for the statistical test needs to be provided for a conclusion d) Not Enough Information;this would depend on the type of statistical test used

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Q1. The correct answer is d) $17.84\leqslant \mu \leqslant 26.16$. To calculate the 95% confidence interval for the population mean, we use the formula $\bar{x} \pm z \cdot \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the critical value for the desired confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. In this case, $\bar{x} = 22$, $z = 1.96$ (for a 95% confidence level), $\sigma = \sqrt{45}$, and $n = 10$. Plugging in these values, we get $22 \pm 1.96 \cdot \frac{\sqrt{45}}{\sqrt{10}}$, which simplifies to $17.84\leqslant \mu \leqslant 26.16$. Q2. The correct answer is d) $0.178\leqslant p\leqslant 0.232$. To construct a 95% confidence interval for the population proportion, we use the formula $\hat{p} \pm z \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p}$ is the sample proportion, $z$ is the critical value for the desired confidence level, and $n$ is the sample size. In this case, $\hat{p} = 0.18$, $z = 1.96$ (for a 95% confidence level), and $n = 1220$. Plugging in these values, we get $0.18 \pm 1.96 \cdot \sqrt{\frac{0.18(1-0.18)}{1220}}$, which simplifies to $0.178\leqslant p\leqslant 0.232$. Q3. The correct answer is b) 0.9082. To find the probability that the subject's ammonia concentration is between 292 and 649 ppb, we need to calculate the area under the normal distribution curve between these two values. We can use the standard normal distribution table or a calculator to find this probability. The z-scores for 292 and 649 are $\frac{292-491}{119}$ and $\frac{649-491}{119}$, respectively. Using the standard normal distribution table or a calculator, we find that the probability is approximately 0.9082. Q4. The correct answer is c) Sometimes True; the p-value for the statistical test needs to be provided for a conclusion. The statement is not always true because it depends on the p-value obtained from the statistical test. If the p-value is greater than or equal to 0.10 and less than or equal to 0.05, then there is not sufficient evidence to reject the null hypothesis at the 5% level, even if there is sufficient evidence to reject it at the 10% level. Therefore, the correct answer is c) Sometimes True; the p-value for the statistical test needs to be provided for a conclusion.

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