Statistics Worksheet

**Page 1**

1.

A retail garment shop receives a shipment of trousers, with a standard length of 49.0 in. and a standard deviation of 1.0 inch. A random sample of 32 trousers had a mean length of 48.8 in. Find the 95% confidence interval.

a. | The interval between 48.65 and 49.35 | ||

b. | The interval between 32 and 49 | ||

c. | The interval between 48.8 and 49.9 | ||

d. | None of the above |

[Replace σ = 1 and

μ - 1.96

μ + 1.96

The 95% confidence interval is the interval between 48.65 and 49.35.

Correct answer : (1)

2.

A retail garment shop receives a shipment of trousers, with a standard length of 49.0 in. and a standard deviation of 1.0 inch. A random sample of 32 trousers had a mean length of 48.8 in. Which of the following statements is true?

a. | The sample mean does not lie with in the 95% confidence interval | ||

b. | The sample mean lies with in the 95% confidence interval |

[Replace σ = 1 and

μ - 1.96

μ + 1.96

The 95% confidence interval is the interval between 48.65 and 49.35.

48.65 < 48.8 < 49.35, which is true.

[Sample mean is 48.8.]

The sample mean 48.8, lies within the 95% confidence interval.

Correct answer : (2)

3.

The mean score on a standardized test is 100 with a standard deviation of 8. A random sample of 48 scores was found to have a mean of 98. Find the standard error.

a. | 1.15 | ||

b. | 0.8 | ||

c. | 8.0 | ||

d. | 1.0 |

[Use Standard error formula.]

[Replace σ = 8,

Correct answer : (1)

4.

The mean score on a standardized test is 100 with a standard deviation of 8. A random sample of 48 scores was found to have a mean of 98. Find the 95% confidence interval.

a. | The interval is between 97.75 and 102.25 | ||

b. | The interval is between 1.15 and 100 | ||

c. | The interval is between 100 and 98 | ||

d. | The interval is between 79.75 and 20.25 |

μ - 1.96

μ + 1.96

The 95% confidence interval is between 97.75 and 102.25.

Correct answer : (1)

5.

To find out how much time is spent at meals by the children of the United States, all the children in a locality of Chicago are interviewed. Which of the statements is true?

a. | The children in a locality of Chicago represents a random sample of the population for this study | ||

b. | The children in a locality of Chicago represents the population for this study | ||

c. | Both of the above | ||

d. | None of the above |

Correct answer : (1)

6.

In order to find the mean weight of elephants in a zoo, the weights of all the elephants were measured and the mean calculated. State which of the statements is true.

a. | The group of elephants chosen represents the population for this study. | ||

b. | The group of elephants chosen represents a random sample of the population for this study. | ||

c. | Both of the above | ||

d. | None of the above |

Correct answer : (1)

7.

To find the average height of an oak tree, a set of full grown oak trees from a forest were identified and their heights measured. Which of the following statements is true?

a. | The set of full grown oak trees from a forest represent the population for this study | ||

b. | The set of full grown oak trees from a forest represent a random sample of the population for this study | ||

c. | Both are true | ||

d. | Neither is true |

Correct answer : (2)

8.

To find out the most popular brand of ice-cream in Florida, all the orders placed for ice cream in an ice-cream parlour in Miami were recorded. Which of the statements is true?

a. | The orders placed for ice-cream in an ice cream parlour in Miami represents the population for this study | ||

b. | The orders placed in an ice-cream parlour in Miami does not represent a random sample of the population for this study | ||

c. | Both of the above | ||

d. | None of the above |

Correct answer : (4)

9.

A company makes wooden wardrobes having a standard height of 55 in., with a standard deviation of 2.5 in. In a random sample of 23 wardrobes, 6 wardrobes measured 58.5 in., 8 wardrobes measured 53.8 in. and 9 wardrobes measured 56 in. State the null hypothesis(H_{o}) and the alternative hypothesis(H_{$a$}) for the problem.

a. | H _{o}: Mean height of a wardrobe = 55.8 in.H _{$a$} Mean height of a wardrobe ≠ 55.8 in. | ||

b. | H _{o}: Mean height of a wardrobe ≠53.8 in.H _{$a$}: Mean height of a wardrobe = 53.8 in. | ||

c. | H _{o}: Mean height of a wardrobe ≠55 in.H _{$a$}: Mean height of a wardrobe = 55 in. | ||

d. | H _{o}: Mean height of a wardrobe = 55 in.H _{$a$}: Mean height of a wardrobe ≠ 55 in. |

H

H

Correct answer : (4)

10.

A company makes wooden wardrobes having a standard height of 55 in., with a standard deviation of 2.5 in. In a random sample of 23 wardrobes, 6 wardrobes measured 58.5 in., 8 wardrobes measured 53.8 in. and 9 wardrobes measured 56 in.. Find the 95% confidence interval.

a. | The interval is between 53.2 and 56.2 | ||

b. | The interval is between 53.98 and 56.02 | ||

c. | The interval is between 0 and 55 | ||

d. | The interval is betwee 55 and 60 |

[Where μ = The population mean.]

Standard error,

[Replace σ = 2.5 and

μ - 1.96

μ + 1.96

The 95% confidence interval is between 53.98 and 56.02

Correct answer : (2)