Question

Q1- In the Super-Mega lottery there are 50 numbers (1 to 50), a player chooses ten different numbers and hopes that these get drawn. If the player's numbers get drawn, he/she wins an obscene amount of money. The table below displays the frequency with which classes of numbers are chosen (not drawn). These numbers came from a sample of 194 chosen numbers.

Chosen Numbers (n=194) | |||||

1 to 10 | 11 to 20 | 21 to 30 | 31 to 40 | 41 to 50 | |

Count | 46 | 39 | 32 | 24 | 53 |

Test the claim that chosen numbers are not evenly distributed across the five classes. Test this claim at the 0.05 significance level.

(a) Find the test statistic.=

(b) Find the critical value.=

Q2-

The number of men and women among professors in Math, Physics, Chemistry, Linguistics, and English departments from a SRS of small colleges were counted, and the results are shown in the table below.

Dept. | Math | Physics | Chemistry | Linguistics | English |

Men | 70 | 89 | 34 | 24 | 42 |

Women | 6 | 5 | 8 | 14 | 17 |

Test the claim that the gender of a professor is independent of the department. Use the significance level α=0.01

(a) The test statistic is χ2=

(b) The critical value is χ2=

Answer #1

Choosing Lottery Numbers: In the Super-Mega
lottery there are 50 numbers (1 to 50), a player chooses ten
different numbers and hopes that these get drawn. If the player's
numbers get drawn, he/she wins an obscene amount of money. The
table below displays the frequency with which classes of numbers
are chosen (not drawn). These numbers came from a sample of 180
chosen numbers.
Chosen Numbers (n = 180)
1
to 10
11
to 20
21
to 30
31
to...

(1 point) The number of men and women among professors in Math,
Physics, Chemistry, Linguistics, and English departments from a SRS
of small colleges were counted, and the results are shown in the
table below.
Dept.
Math
Physics
Chemistry
Linguistics
English
Men
53
125
49
27
57
Women
10
10
6
14
36
Test the claim that the gender of a professor is independent of
the department. Use the significance level α=0.025α=0.025
(a) The test statistic is χ2=
(b) The...

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