QUESTION 1 a) What is the difference between descriptive statistics and inferential statistics? b) The table below shows the age distribution of a sample of 150 students at UCC. Find an estimate of...

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QUESTION 1 a) What is the difference between descriptive statistics and inferential statistics? b) The table below shows the age distribution of a sample of 150 students at UCC. Find an estimate of the variance and standard deviation. Age Number 25 - 34 33 35 - 44 39 45 - 54 48 55 - 64 30 QUESTION 2 A population consists of the following three values: 4, 5, and 6. a) Carry out a sampling with replacement and list all possible samples of size 2 and compute the mean of every sample. (2 Marks) b) Calculate the means of the distribution of the sample mean and the population mean. Compare the two values. (6 Marks) QUESTION 3 JamSoft, a computer games development company plans to roll out a new educational game software for Jamaica elementary schools. However, they need to ascertain the production time (measured in labor-hours) to produce the game software. For a random sample of 20 computer games, the mean time is found to be 40,000 labor-hours. The population standard deviation is known to be 5000 labor-hours and the distribution of production times is normal. a) Construct a 98% confidence interval for the mean production time to produce a computer game. (5 Marks) b) Explain why we need to make the confidence interval. Why is it not correct to say that the average production time needed to produce all computer games is 40,000 labor-hours? (3 Marks) QUESTION 4 A report shows that the average cost of tuition and fees at a four-year university is $5,820. A researcher believes the average cost is actually higher than $5,820. She selects a random sample of 46 universities and finds the mean to be $6,100, with standard deviation of $759. a) Formulate the null and alternative hypotheses. (2 Marks) b) Is there enough evidence to support the researcher’s claim at the 5% level of significance (6 Marks) QUESTION 5 a) A MTH201 test was given at the UCC Kingston Campus. There were 15 multiple choice questions. Each question had 4 answers to choose from. A student needs at least 10 correct answers to pass the test. Find the probability that the students pass. (4 Marks) b) A truck hire company receives an average request of two trucks per day. Find the probability that on a given day there are at most two requests for truck drivers. (4 Marks) QUESTION 1 a) What is the difference between descriptive statistics and inferential statistics? b) The table below shows the age distribution of a sample of 150 students at UCC. Find an estimate of the variance and standard deviation. Age Number 25 - 34 33 35 - 44 39 45 - 54 48 55 - 64 30 QUESTION 2 A population consists of the following three values: 4, 5, and 6. a) Carry out a sampling with replacement and list all possible samples of size 2 and compute the mean of every sample. (2 Marks) b) Calculate the means of the distribution of the sample mean and the population mean. Compare the two values. (6 Marks) QUESTION 3 JamSoft, a computer games development company plans to roll out a new educational game software for Jamaica elementary schools. However, they need to ascertain the production time (measured in labor-hours) to produce the game software. For a random sample of 20 computer games, the mean time is found to be 40,000 labor-hours. The population standard deviation is known to be 5000 labor-hours and the distribution of production times is normal. a) Construct a 98% confidence interval for the mean production time to produce a computer game. (5 Marks) b) Explain why we need to make the confidence interval. Why is it not correct to say that the average production time needed to produce all computer games is 40,000 labor-hours? (3 Marks) QUESTION 4 A report shows that the average cost of tuition and fees at a four-year university is $5,820. A researcher believes the average cost is actually higher than $5,820. She selects a random sample of 46 universities and finds the mean to be $6,100, with standard deviation of $759. a) Formulate the null and alternative hypotheses. (2 Marks) b) Is there enough evidence to support the researcher’s claim at the 5% level of significance (6 Marks) QUESTION 5 a) A MTH201 test was given at the UCC Kingston Campus. There were 15 multiple choice questions. Each question had 4 answers to choose from. A student needs at least 10 correct answers to pass the test. Find the probability that the students pass. (4 Marks) b) A truck hire company receives an average request of two trucks per day. Find the probability that on a given day there are at most two requests for truck drivers. (4 Marks)