# Sample size and Hypothesis testing problems

Assignment 3
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at
the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some
give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive
numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the
frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and
tested. Find the temperature reading corresponding to the given information.
1) If 9% of the thermometers are rejected because they have readings that are too low, but all
other thermometers are acceptable, find the temperature that separates the rejected
thermometers from the others.
1)
Assume that X has a normal distribution, and find the indicated probability.
2) The mean is &#956; = 60.0 and the standard deviation is &#963; = 4.0.
Find the probability that X is less than 53.0.
2)
Find the indicated probability.
3) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz
and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a
randomly selected bottle will be less than 32 oz?
3)
1
Solve the problem.
4) A history teacher assigns letter grades on a test according to the following scheme:
A: Top 10%
B: Scores below the top 10% and above the bottom 60%
C: Scores below the top 40% and above the bottom 20%
D: Scores below the top 80% and above the bottom 10%
F: Bottom 10%
Scores on the test are normally distributed with a mean of 69 and a standard deviation of
13.4. Find the numerical limits for each letter grade.
4)
5) The weights of the fish in a certain lake are normally distributed with a mean of 12 lb and a
standard deviation of 12. If 16 fish are randomly selected, what is the probability that the
mean weight will be between 9.6 and 15.6 lb?
5)
Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
6) Two percent of hair dryers produced in a certain plant are defective. Estimate the
probability that of 10,000 randomly selected hair dryers, exactly 225 are defective.
6)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
7) Of 132 adults selected randomly from one town, 33 of them smoke. Construct a 99%
confidence interval for the true percentage of all adults in the town that smoke.
7)
2
Use the given degree of confidence and sample data to construct a confidence interval for the population mean &#956;. Assume
that the population has a normal distribution.
8) The amounts (in ounces) of juice in eight randomly selected juice bottles are:
15.0 15.9 15.3 15.3
15.5 15.9 15.9 15.0
Construct a 98 percent confidence interval for the mean amount of juice in all such bottles.
8)
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation &#963;.
Assume that the population has a normal distribution.
9) College students' annual earnings: 98% confidence; n = 9, x = \$3262, s = \$836 9)
Find the minimum sample size you should use to assure that your estimate of p
^
will be within the required margin of
error around the population p.
10) Margin of error: 0.007; confidence level: 99%; from a prior study, p
^
is estimated by 0.238 10)
3

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Solution Summary

The solution provides step by step method for the calculation of sample size and test statistic . Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

\$2.19
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Basil Sunny, MSc

Rating 4.9/5

Active since 2008

BSc, Mahatma Gandhi University Kottayam, India
MSc, Mahatma Gandhi University Kottayam, India
PhD (IP), Mahatma Gandhi University Kottayam, India

Responses 2624

"Thank you for the help. Can you show me how you got Critical values = ±2.575829304? I'm having a hard time finding how to get this. Thanks!"

"Thanks great help"

"Hi thanks for the excel format explanation, it makes it easy for me to understand."

"how exactly do you get = 0.1655 + 0.1146 + … + 0.0001 = P (X ≥ 12) = P (X = 12) + P (X = 13) + … + P (X = 18) = 0.1655 + 0.1146 + … + 0.0001 = 0.3743"

"Thanks for the great explanation and the excel fine."

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• assignment.pdf

Assignment 3

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 °C at
the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some
give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive
numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the
frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and
tested. Find the temperature reading corresponding to the given information.
1) If 9% of the thermometers are rejected because they have readings that are too low, but all 1)
other thermometers are acceptable, find the temperature that separates the rejected
thermometers from the others.

Assume that X has a normal distribution, and find the indicated probability.
2) The mean is μ = 60.0 and the standard deviation is σ = 4.0. 2)
Find the probability that X is less than 53.0.

Find the indicated probability.
3) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz 3)
and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a
randomly selected bottle will be less than 32 oz?

1
Solve the problem.
4) A history teacher assigns letter grades on a test according to the following scheme: 4)
A: Top 10%
B: Scores below the top 10% and above the bottom 60%
C: Scores below the top 40% and above the bottom 20%
D: Scores below the top 80% and above the bottom 10%
F: Bottom 10%
Scores on the test are normally distributed with a mean of 69 and a standard deviation of
13.4. Find the numerical limits for each letter grade.

5) The weights of the fish in a certain lake are normally distributed with a mean of 12 lb and a 5)
standard deviation of 12. If 16 fish are randomly selected, what is the probability that the
mean weight will be between 9.6 and 15.6 lb?

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
6) Two percent of hair dryers produced in a certain plant are defective. Estimate the 6)
probability that of 10,000 randomly selected hair dryers, exactly 225 are defective.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
7) Of 132 adults selected randomly from one town, 33 of them smoke. Construct a 99% 7)
confidence interval for the true percentage of all adults in the town that smoke.

2
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume
that the population has a normal distribution.
8) The amounts (in ounces) of juice in eight randomly selected juice bottles are: 8)
15.0 15.9 15.3 15.3
15.5 15.9 15.9 15.0
Construct a 98 percent confidence interval for the mean amount of juice in all such bottles.

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ .
Assume that the population has a normal distribution.
9) College students' annual earnings: 98% confidence; n = 9, x = \$3262, s = \$836 9)

^
Find the minimum sample size you should use to assure that your estimate of p will be within the required margin of
error around the population p.
^
10) Margin of error: 0.007; confidence level: 99%; from a prior study, p is estimated by 0.238 10)

3