Question

The population standard deviation for the heights of dogs, in inches, in a city is 7.8 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?

z0.10 | z0.05 | z0.04 | z0.025 | z0.01 | z0.005 |
---|---|---|---|---|---|

1.282 | 1.645 | 1.751 | 1.960 | 2.326 | 2.576 |

Use the table above for the z-score, and be sure to round up to the nearest integer.

Provide your answer below:

Answer #1

Solution :

Given that,

Population standard deviation = = 7.8

Margin of error = E = 2

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2}
= Z_{0.025} = 1.960

sample size = n = (Z_{/2}*
/ E) ^{2}

n = (1.960 * 7.8/ 2)^{2}

n = 58.43

n = 59

**Sample size = 59**

**The minimum sample size that can be taken is
59.**

he population standard deviation for the heights of dogs, in
inches, in a city is 6.5 inches. If we want to be 95% confident
that the sample mean is within 2 inches of the true population
mean, what is the minimum sample size that can be taken? z0.10
z0.05 z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576
Use the table above for the z-score, and be sure to round up to the
nearest integer.

The population standard deviation for the heights of dogs in
inches in a city is 3.9 inches. If we want to be 90% confident that
the sample mean is within 2 inches of the true population mean.
What is the minimum sample size that can be taken?
Z0.10
1.282
Z0.05
1.645
Z0.025
1.960
Z.0.01
2.326
Z0.005
2.576

The lengths of text messages are normally distributed with a
population standard deviation of 4 characters and an unknown
population mean. If a random sample of 27 text messages is taken
and results in a sample mean of 23 characters, find a 95%
confidence interval for the population mean. Round your answers to
two decimal places.
z0.10
z0.05
z0.04
z0.025
z0.01
z0.005
1.282
1.645
1.751
1.960
2.326
2.576

The lengths of text messages are normally distributed with a
population standard deviation of 3 characters and an unknown
population mean. If a random sample of 29 text messages is taken
and results in a sample mean of 30characters, find a 92% confidence
interval for the population mean. Round your answers to two decimal
places
z0.10
z0.05
z0.04
z0.025
z0.01
z0.005
1.282
1.645
1.751
1.960
2.326
2.576
select the correct answer below:
(28.56,31.44)
(29.29,30.71)
(29.08,30.92)
(28.70,31.30)
(29.02,30.98)
(28.91,31.09)

The lengths of text messages are normally distributed with a
population standard deviation of 3 characters and an unknown
population mean. If a random sample of 26 text messages is taken
and results in a sample mean of 29 characters, find a 98%
confidence interval for the population mean. Round your answers to
two decimal places. z0.10 z0.05 z0.04 z0.025 z0.01 z0.005 1.282
1.645 1.751 1.960 2.326 2.576 You may use a calculator or the
common z-values above. Select the...

Suppose the manager of a shoe store wants to determine the
current percentage of customers who are males. How many customers
should the manager survey in order to be 98% confident that the
estimated (sample) proportion is within 5 percentage points of the
true population proportion of customers who are males? z0.10 z0.05
z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576 Use
the table of values above?

Suppose the manager of a shoe store wants to determine the
current percentage of customers who are males. How many customers
should the manager survey in order to be 92% confident that the
estimated (sample) proportion is within 5 percentage points of the
true population proportion of customers who are males?
z0.10
z0.05
z0.04
z0.025
z0.01
z0.005
1.282
1.645
1.751
1.960
2.326
2.576
Use the table of values above.

Suppose the manager of a shoe store wants to determine the
current percentage of customers who are males. How many customers
should the manager survey in order to be 99% confident that the
estimated (sample) proportion is within 5 percentage points of the
true population proportion of customers who are males?
z0.10
z0.05
z0.04
z0.025
z0.01
z0.005
1.282
1.645
1.751
1.960
2.326
2.576
Use the table of values above.

Suppose the manager of a shoe store wants to determine the
current percentage of customers who are males. How many customers
should the manager survey in order to be 80% confident that the
estimated (sample) proportion is within 6 percentage points of the
true population proportion of customers who are males?
z0.10
z0.05
z0.04
z0.025
z0.01
z0.005
1.282
1.645
1.751
1.960
2.326
2.576
Use the table of values above.

Suppose the manager of a shoe store wants to determine the
current percentage of customers who are males. How many customers
should the manager survey in order to be 95% confident that the
estimated (sample) proportion is within 6 percentage points of the
true population proportion of customers who are males?
z0.10
z0.05
z0.04
z0.025
z0.01
z0.005
1.282
1.645
1.751
1.960
2.326
2.576
Use the table of values above.
Provide your answer below:

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