Question

1.A weekend TV game show called rolling a dice is running each
week. For each roll, if the dice shows an odd number the
participate earns 5 dollars and otherwise, he gets nothing. Each
participate can roll the dice 20 times. Let X denote the number
times the dice shows an odd number.

a) (2 mark) Calculate the average earning of a
participate.

b) Calculate the probability that ? ⩽ 2 (show your
final answer correct to four decimal places).

c) Under appropriate condition, a Binomial random
variable X can be approximated by a Normal random variable Y with
the same mean and standard deviation. In doing so, we need to apply
a continuity correction. That is

? (? ⩽ ?) ≈ ? (? ⩽ ? + 0.5).

Calculating the probability that ? ≤ 6 by using Normal
approximation with

continuity correction.

2. A manufacturer is interested in estimating the lifetime of
printers. A confidence interval is constructed based on a sample of
20 printers and the assumption that the population distribution of
the lifetime of a printer is normal.

a) If the population standard deviation is 1.5 and
the upper end of a 95% confidence interval is 6.36, find the
observed sample mean (show your final answer correct to two decimal
places).

b) If, instead, we only know the sample standard
deviation (which is 1.2), and given the lower end of a 90%
confidence interval (which is 3.14), find the observed sample mean
(show your final answer correct to two decimal places).

c) Given the significance level β= 0.1, and the
sample standard deviation is s = 1.2, perform a hypothesis testing
(with detailed steps) to test if the population variance ?2 =
1.8.

Answer #1

A manufacturer is interested in
estimating the lifetime of printers. A confidence interval is
constructed based on a sample of 20 printers and the assumption
that the population distribution of the lifetime of a printer is
normal.
If the population standard deviation is 1.5 and the
upper end of a 95% confidence interval is 6.36, find the observed
sample mean (show your final answer correct to two decimal
places).
If, instead, we only know the sample standard
deviation (which is...

The Fox TV network is considering replacing one of its
prime-time crime investigation shows with a new family-oriented
comedy show. Before a final decision is made, network executives
commission a sample of 370 viewers. After viewing the comedy, 260
indicated they would watch the new show and suggested it replace
the crime investigation show.
a. Estimate the value of the population
proportion. (Round the final answer to 3 decimal
places.)
Estimate of proportion ______
b. Compute the standard error of...

*Please Answer All *
1. A company has developed a new type of light bulb and wants to
estimate its mean lifetime. A simple random sample of 12 bulbs had
a sample mean lifetime of 651 hours with a sample standard
deviation of 31 hours. It is reasonable to believe that the
population is approximately normal. Find the lower bound of the 95%
confidence interval for the population mean lifetime of all bulbs
manufactured by this new process. Round to...

A sample of 23 observations is selected from a normal population
where the sample standard deviation is 4.95. The sample mean is
16.90.
a. Determine the standard error of the mean.
(Round the final answer to 2 decimal places.)
The standard error of the mean is _______ .
b. Determine the 90% confidence interval for
the population mean. (Round the t-value to 3
decimal places. Round the final answers to 3 decimal
places.)
The 90% confidence interval for the population...

A sample of 25 observations is selected from a normal population
where the population standard deviation is 32. The sample mean is
77.
a.
Determine the standard error of the mean. (Round the final
answer to 3 decimal places.)
The standard error of
the mean is .
b.
Determine the 95% confidence interval for the population mean.
(Round the z-value to 2 decimal places. Round the
final answers to 3 decimal places.)
The 95% confidence
interval for the population mean...

A sample of 28 observations is selected from a normal population
where the sample standard deviation is 5.00. The sample mean is
16.95.
a. Determine the standard error of the mean.
(Round the final answer to 2 decimal places.)
The standard error of the mean is.
b. Determine the 95% confidence interval for
the population mean. (Round the t-value to 3
decimal places. Round the final answers to 3 decimal
places.)
The 95% confidence interval for the population mean is...

A sample of 25 observations is selected from a normal population
where the sample standard deviation is 4.85. The sample mean is
16.80.
a. Determine the standard error of the mean.
(Round the final answer to 2 decimal places.)
The standard error of the mean is
.
b. Determine the 95% confidence interval for
the population mean. (Round the t-value to 3
decimal places. Round the final answers to 3 decimal
places.)
The 95% confidence interval for the population...

A sample of 28 observations is selected from a normal population
where the sample standard deviation is 4.40. The sample mean is
16.40.
a. Determine the standard error of the mean.
(Round the final answer to 2 decimal places.)
The standard error of the mean is
.
b. Determine the 98% confidence interval for
the population mean. (Round the t-value to 3
decimal places. Round the final answers to 3 decimal
places.)
The 98% confidence interval for the population...

A sample of 29 observations is selected from a normal population
where the population standard deviation is 40. The sample mean is
89.
a. Determine the standard error of the mean.
(Round the final answer to 3 decimal places.)
The standard error of the mean is .
b. Determine the 98% confidence interval for
the population mean. (Round the z-value to 2
decimal places. Round the final answers to 3 decimal
places.)
The 98% confidence interval for the population mean is...

Exercise 8-2 A sample of 43 observations is taken from a normal
population with a standard deviation of 24. The sample mean is 43.
Determine the 80% confidence interval for the population mean.
(Round the final answers to 3 decimal places.) Confidence interval
for the population mean is and .
statistics

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