statistics one proportion z test


A statistical hypothesis is an assumption about a population which may or may not be true. Hypothesis testing is a set of formal procedures used by statisticians to either accept or reject statistical hypotheses. Statistical hypotheses are of two types:

  • Null hypothesis, ${H_0}$ – represents a hypothesis of chance basis.
  • Alternative hypothesis, ${H_a}$ – represents a hypothesis of observations which are influenced by some non-random cause.

Example

suppose we wanted to check whether a coin was fair and balanced. A null hypothesis might say, that half flips will be of head and half will of tails whereas alternative hypothesis might say that flips of head and tail may be very different.

$ H_0: P = 0.5 \\[7pt]
H_a: P \ne 0.5 $

For example if we flipped the coin 50 times, in which 40 Heads and 10 Tails results. Using result, we need to reject the null hypothesis and would conclude, based on the evidence, that the coin was probably not fair and balanced.

Hypothesis Tests

Following formal process is used by statistican to determine whether to reject a null hypothesis, based on sample data. This process is called hypothesis testing and is consists of following four steps:

  1. State the hypotheses – This step involves stating both null and alternative hypotheses. The hypotheses should be stated in such a way that they are mutually exclusive. If one is true then other must be false.
  2. Formulate an analysis plan – The analysis plan is to describe how to use the sample data to evaluate the null hypothesis. The evaluation process focuses around a single test statistic.
  3. Analyze sample data – Find the value of the test statistic (using properties like mean score, proportion, t statistic, z-score, etc.) stated in the analysis plan.
  4. Interpret results – Apply the decisions stated in the analysis plan. If the value of the test statistic is very unlikely based on the null hypothesis, then reject the null hypothesis.

Table of Contents
1.statistics adjusted rsquared

2.statistics analysis of variance

3.statistics arithmetic mean

4.statistics arithmetic median

5.statistics arithmetic mode

6.statistics arithmetic range

7.statistics bar graph

8.statistics best point estimation

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12.statistics boxplots

13.statistics central limit theorem

14.statistics chebyshevs theorem

15.statistics chisquared distribution

16.statistics chi squared table

17.statistics circular permutation

18.statistics cluster sampling

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20.statistics combination

21.statistics combination with replacement

22.statistics comparing plots

23.statistics continuous uniform distribution

24.statistics cumulative frequency

25.statistics coefficient of variation

26.statistics correlation coefficient

27.statistics cumulative plots

28.statistics cumulative poisson distribution

29.statistics data collection

30.statistics data collection questionaire designing

31.statistics data collection observation

32.statistics data collection case study method

33.statistics data patterns

34.statistics deciles statistics

35.statistics dot plot

36.statistics exponential distribution

37.statistics f distribution

38.statistics f test table

39.statistics factorial

40.statistics frequency distribution

41.statistics gamma distribution

42.statistics geometric mean

43.statistics geometric probability distribution

44.statistics goodness of fit

45.statistics grand mean

46.statistics gumbel distribution

47.statistics harmonic mean

48.statistics harmonic number

49.statistics harmonic resonance frequency

50.statistics histograms

51.statistics hypergeometric distribution

52.statistics hypothesis testing

53.statistics interval estimation

54.statistics inverse gamma distribution

55.statistics kolmogorov smirnov test

56.statistics kurtosis

57.statistics laplace distribution

58.statistics linear regression

59.statistics log gamma distribution

60.statistics logistic regression

61.statistics mcnemar test

62.statistics mean deviation

63.statistics means difference

64.statistics multinomial distribution

65.statistics negative binomial distribution

66.statistics normal distribution

67.statistics odd and even permutation

68.statistics one proportion z test

69.statistics outlier function

70.statistics permutation

71.statistics permutation with replacement

72.statistics pie chart

73.statistics poisson distribution

74.statistics pooled variance r

75.statistics power calculator

76.statistics probability

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78.statistics probability multiplicative theorem

79.statistics probability bayes theorem

80.statistics probability density function

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82.statistics process sigma

83.statistics quadratic regression equation

84.statistics qualitative data vs quantitative data

85.statistics quartile deviation

86.statistics range rule of thumb

87.statistics rayleigh distribution

88.statistics regression intercept confidence interval

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90.statistics reliability coefficient

91.statistics required sample size

92.statistics residual analysis

93.statistics residual sum of squares

94.statistics root mean square

95.statistics sample planning

96.statistics sampling methods

97.statistics scatterplots

98.statistics shannon wiener diversity index

99.statistics signal to noise ratio

100.statistics simple random sampling

101.statistics skewness

102.statistics standard deviation

103.statistics standard error se

104.statistics standard normal table

105.statistics statistical significance

106.statistics formulas

107.statistics notations

108.statistics stem and leaf plot

109.statistics stratified sampling

110.statistics student t test

111.statistics sum of square

112.statistics tdistribution table

113.statistics ti 83 exponential regression

114.statistics transformations

115.statistics trimmed mean

116.statistics type i amp ii errors

117.statistics variance

118.statistics venn diagram

119.statistics weak law of large numbers

120.statistics z table

121.discuss statistics


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