In: Math

2. What is the sample size, n, for a 95% confidence interval on the mean, if we know that the process’ standard error is 3.2 units, and we want to allow at most 1.0 units for our error?

3. Let’s say that you just randomly pulled 32 widgets from your production line and you determined that you need a sample size of 46 widgets, However, you get delayed in being able to pull another bunch of widgets from the line until the start of the next day. How many widgets should you now pull for your analysis?

4. What is the sample size, n, for a 98% confidence interval on the mean, if we know that the process’ standard error is 3.2 units, and we want to allow at most 0.5 units for our error?

5. What is the sample size, n, for a 95% confidence interval on the mean, if we know that the process’ standard error is 3.2 units, and we want to allow at most 0.5 units for our error?

2)

for 95 % CI value of z= | 1.960 |

standard deviation σ= | 3.2 |

margin of error E = | 1 |

required sample size
n=(zσ/E)^{2 }
= |
40.0 |

3)

46 widgets ;as it will remain same to avoid bias

4)

for 98 % CI value of z= | 2.33 |

standard deviation σ= | 3.2 |

margin of error E = | 0.5 |

required sample size
n=(zσ/E)^{2 }
= |
223.0 |

( try 222 if this comes wrong)

5)

for 95 % CI value of z= | 1.96 |

standard deviation σ= | 3.2 |

margin of error E = | 0.5 |

required sample size
n=(zσ/E)^{2 }
= |
158.0 |

The 95% confidence interval for the mean, calculated from a
sample of size n = 25 is 2.233163 ≤ μ ≤ 3.966837 . Determine the
sample mean X ¯ = (round to the first decimal place). Assuming that
the data is normally distributed, determine the sample standard
deviation s = (round to the first decimal place)

Q1.
Explain what happens to the 95 % confidence interval as the
sample size increases.
Explain what happens to the width of the confidence interval
for a 99% interval versus a 95%.
Q2. Consider the population of adult females resident in
Melbourne. Our focus is on the population mean height. Assume we do
not know ? (population standard deviation) or the
population mean, µ. We take a sample of adult females resident in
Melbourne (n=100) and calculate the sample mean...

Determine the sample size n needed to construct a 95?%
confidence interval to estimate the population proportion for the
following sample proportions when the margin of error equals
55?%.
a. p? = 0.50
b. p = 0.60
c. p = 0.70

Determine the sample size n needed to construct a 95%
confidence interval to estimate the population mean for the
following margins of error when sigma equals 67.
a) 25 b) 40 c) 50

Determine the sample size n needed to construct a 95%
confidence interval to estimate the population proportion for the
following sample proportions when the margin of error equals
4%.
a. p over bar equals 0.10
b. p over bar equals 0.20
c. p over bar equals 0.30

14. A researcher estimates the 95% Confidence Interval for a
sample (n=100) with a mean of M=3. The population mean and standard
deviation are known as 2.5±2 (µ±σ). What is the upper confidence
limit for this interval? A) 0.392 B) 1.96 C) 2.608 D) 3.392 E)
There is not enough information to answer this question.

A random sample of size n=500 yielded p̂ =0.08
a) Construct a 95% confidence interval for p.
b) Interpret the 95% confidence interval.
c) Explain what is meant by the phrase "95% confidence
interval."

The 99% confidence interval for the mean, calculated from a
sample of size n = 10 is 0.9390859 ≤ μ ≤ 5.460914 . Determine the
sample mean X ¯ = (round to the first decimal place). Assuming that
the data is normally distributed, determine the sample standard
deviation s = (round to the first decimal place)

[t-interval] If sample mean = 33.6, s = 1.5, sample size is 18.
Determine 95% confidence interval.
Select the closest answer from below
A.
(32.85 , 34.35)
B.
(32.91 , 34.29)
C.
(33.02 , 34.18)
D.
(32.98 , 34.21)

13) What is the minimal sample size needed for a 95% confidence
interval to have a maximal margin of error of 0.1 in the following
scenarios? (Round your answers up the nearest whole number.) (a) a
preliminary estimate for p is 0.28 (b) there is no preliminary
estimate for p

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