Statistical Methods-Tests of Significance (ISS Statistics Paper I (Old Subjective Pattern)): Questions 10 - 14 of 17

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Question number: 10

» Statistical Methods » Tests of Significance » Chi-Square

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Explain how to carry out the chi-squared test for Equation on the basis of a random sample

X 1, X 2, …, X n from N (µ, σ 2) population.

Explanation

Given that a random sample X 1, X 2, …, X n from N (µ, σ 2) population. The hypothesis is

Equation

The null hypothesis is test by chi-square test only assume the sample size is less than 30.

For this we use the likelihood ratio test… (107 more words) …

Question number: 11

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2012

Essay Question▾

Describe in Detail

125out of 285 college-going male students in 1995 from a city were found to be smokers. Another sample of 325 such students from the same city in 2012 included 95 smokers. Examine at 5 % level of significance if smoking habit among college-going students is on the decrease in this city.

Explanation

The given information can be written as in a table:

Year

Smoker

Non-smoker

Total

1995

125

160

285

2012

95

230

325

Total

220

390

610

Here, the null hypothesis is that the proportion of smoker in this two year is same and the alternative is there is decrease in… (98 more words) …

Question number: 12

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2010

Essay Question▾

Describe in Detail

How large a sample must be taken in order that the probability will be at least 0.95 that X n will be within 0.5 of µ (µ is unknown and σ = l).

Explanation

Here, you would know the standard deviation of a population but not know the mean of that population. So, you want to estimate the mean μ to within a given margin of error in a given confidence interval. The required sample size is

Margin of error E = 0.5,

1-α=0.95… (11 more words) …

Question number: 13

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X 1, X 2, …, X 12 be a random sample from a normal N (µ 1, σ 12) and Y 1, Y 2, …Y 10 be another random sample from normal N (µ 2, σ 22), independently to each other. Carry out an appropriate test for testing

Equation

at 5 % level of significance. It is given that Equation .

Explanation

Let X 1, X 2, …, X 12 be a random sample from a normal N (µ 1, σ 12) and Y 1, Y 2, …Y 10 be another random sample from normal N (µ 2, σ 22), independently to… (87 more words) …

Question number: 14

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2009

Essay Question▾

Describe in Detail

Two set of students were given different teaching methods. Their IQ’s are given below:

Set I

77

74

82

73

87

69

66

80

Set II

72

68

76

68

84

68

61

76

Test whether the two teaching methods differ significantly at 5 % level of significance. (Assume critical value of test statistic to be 1.96)

Explanation

Let X i is random variable of student were given different teaching methods in set I with mean Equation and variance σ 12 and Y j is random variable of student were given different teaching methods in set II with mean Equation and variance σ 22. The… (54 more words) …

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