MTH220 Jan21 CMA01 Jan 2021
Studies have shown that "Melanoma", a form of skin cancer, kills 15% of Americans who suffer from the disease each year.
Consider a sample of 10000 melanoma petients. What is the expected value of y, the number of the 10000 melanoma patients who die of this affliction this year?
Studies have shown that "Melanoma", a form of skin cancer, kills 15% of Americans who suffer from the disease each year.
Consider a sample of 10000 melanoma petients. What is the variance of y, the number of the 10000 melanoma patients who die of this affliction this year?
Studies have shown that "Melanoma", a form of skin cancer, kills 15% of Americans who suffer from the disease each year.
Consider a sample of 10000 melanoma patients. What is the probability that y will exceed 1600 patients per year?
It is important to model machine downtime correctly in simulation studies.
Consider a single-machine-tool system with repair times (in minutes) that can be modeled by an exponential distribution mean = 60.
Of interest is the mean repair time of a sample of 100 machine breakdowns.
What is the probability that the mean repair time is no longer than 30 minutes?
It is important to model machine downtime correctly in simulation studies.
Consider a single-machine-tool system with repair times (in minutes) that can be modeled by an exponential distribution mean = 60.
Of interest is the mean repair time of a sample of 100 machine breakdowns.
What is the variance of the mean repair time?
Suppose the average cost of a gallon of unleaded fuel at gas stations is $1.897. Assume that the standard deviation of such costs is $0.15.
Suppose a random sample of n = 100 gas stations is selected from the population and the cost per gallon of unleaded fuel is determined for each.
Consider the "sample mean cost per gallon". What is the approximate probability that the sample has a mean fuel cost between $1.90 and $1.92?
The following data from a random sample represents the average daily energy intake in kJ for each of eleven healthy women:
5260 5470 5640 6180 6390 6515 6805 7515 7515 8230 8770
Interest centred on comparing these data with an underlying mean daily energy intake of 7725 kJ This was the recommended daily intake. Departures from this mean in either direction were considered to be of interest. Assuming that the population is normal and the population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of significance was conducted. The null hypothesis is H0: m = 7725.
Which test is appropriate to apply for this one population hypothesis problem?
The following data from a random sample represents the average daily energy intake in kJ for each of eleven healthy women:
5260 5470 5640 6180 6390 6515 6805 7515 7515 8230 8770
Interest centred on comparing these data with an underlying mean daily energy intake of 7725 kJ This was the recommended daily intake. Departures from this mean in either direction were considered to be of interest. Assuming that the population is normal and the population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of significance was conducted. The null hypothesis is H0: m = 7725.
What is the value of observed test statistics?
The following data from a random sample represents the average daily energy intake in kJ for each of eleven healthy women:
5260 5470 5640 6180 6390 6515 6805 7515 7515 8230 8770
Interest centred on comparing these data with an underlying mean daily energy intake of 7725 kJ This was the recommended daily intake. Departures from this mean in either direction were considered to be of interest. Assuming that the population is normal and the population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of significance was conducted. The null hypothesis is H0: m = 7725.
What is the degree of freedom df in this problem?
The following data from a random sample represents the average daily energy intake in kJ for each of eleven healthy women:
5260 5470 5640 6180 6390 6515 6805 7515 7515 8230 8770
Interest centred on comparing these data with an underlying mean daily energy intake of 7725 kJ This was the recommended daily intake. Departures from this mean in either direction were considered to be of interest. Assuming that the population is normal and the population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of significance was conducted. The null hypothesis is H0: m = 7725.
In order to make a decision as to whether to accept or reject the null hypothesis, we need to compare the observed test statistic with the critical value. What is this critical value |ta/2| ?
The following data from a random sample represents the average daily energy intake in kJ for each of eleven healthy women:
5260 5470 5640 6180 6390 6515 6805 7515 7515 8230 8770
Interest centred on comparing these data with an underlying mean daily energy intake of 7725 kJ This was the recommended daily intake. Departures from this mean in either direction were considered to be of interest. Assuming that the population is normal and the population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of significance was conducted. The null hypothesis is H0: m = 7725.
What conclusions can be drawn, at the 5% level of significance?
The specifications for a certain kind of ribbon call for a mean breaking strength of 185 pounds. Suppose five pieces are randomly selected from different rolls. The breaking strengths of these ribbons are 171.6, 191.8, 178.3, 184.9 and 189.1 pounds. You are required to perform an appropriate hypothesis test by formulating the null hypothesis m ≥ 185 against the alternative hypothesis m < 185 at a = 0.05.
What is the value of the observed test statistic?
. The specifications for a certain kind of ribbon call for a mean breaking strength of 185 pounds. Suppose five pieces are randomly selected from different rolls. The breaking strengths of these ribbons are 171.6, 191.8, 178.3, 184.9 and 189.1 pounds. You are required to perform an appropriate hypothesis test by formulating the null hypothesis m ≥ 185 against the alternative hypothesis m < 185 at a = 0.05.
What conclusions can be drawn?
Assuming that the height of male students in a large university is normally distributed with mean 172.7cm and variance 57.76cm2. 80 samples each with 25 male students are obtained. In how many samples would you expect the sample mean to be between 169.66cm and 173.46cm? Give you answer to one decimal place.
In each of the 5 levels of treatment in an ANOVA experiment, the sum of the seven observed values (A), and the sum of squares of the seven observed values (B) are recorded as:
Level 1: A = 645, B = 59847
Level 2: A = 721, B = 74609
Level 3: A = 970, B = 134936
Level 4: A = 1017, B = 148367
Level 5: A = 981, B = 138415
What is the value of the F test statistic? Give you answer to 1 decimal place.
A certain machine has been producing washers having a mean thickness of 0.125cm. To determine whether the machine is in proper working order, a sample of 10 washers is chosen for which the mean thickness is 0.133cm and the variance is 0.000064cm2. Estimate the p-value for this hypothesis test to 3 decimal places.
We are interested to compare the hourly wage (in S$) of cooks of high-end restaurants in the Core Central Region (CCR), the Rest of Central Region (RCR), Private Housing Region (PHR), and HDB Estates Region (HDB) of Singapore. From each region, information of five cooks were collected. The following were calculated from the data collected:
(i) Total sum of squares of variation = 745.7
(ii) Mean sum of squares of variation due to treatments = 109.6
Give the test statistic value to 2 decimal places.
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