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The document discusses hypothesis testing procedures. It describes the 7 steps of hypothesis testing which include setting the null and alternative hypotheses, choosing a statistical test, setting the significance level, establishing decision rules, collecting sample data, analyzing the data, and arriving at a statistical conclusion. Common statistical tests mentioned are F-tests, t-tests, and z-tests. The F-test compares variances by taking the ratio and uses sums of squares to develop statistics. The document provides an example of a company collecting potential customer spending data on flats in two areas to estimate differences in population means.
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This document provides an overview of key concepts related to formulating and testing hypotheses. It defines a hypothesis as a proposition or claim about a population that can be empirically tested. Hypothesis testing involves examining two opposing hypotheses: the null hypothesis (H0) and alternative hypothesis (Ha). It describes the basic steps of hypothesis testing as formulating the hypotheses, defining a test statistic, determining the distribution of the test statistic, defining the critical region, and making a decision to accept or reject the null hypothesis. Key concepts like type I and type II errors, significance levels, critical values, and one-tailed vs two-tailed tests are also explained. Parametric tests like the z-test, t-test, and
Testing of hypothesis
This document discusses the process of testing hypotheses. It begins by defining hypothesis testing as a way to make decisions about population characteristics based on sample data, which involves some risk of error. The key steps are outlined as:
1) Formulating the null and alternative hypotheses, with the null hypothesis stating no difference or relationship.
2) Computing a test statistic based on the sample data and selecting a significance level, usually 5%.
3) Comparing the test statistic to critical values to either reject or fail to reject the null hypothesis.
Examples are provided to demonstrate hypothesis testing for a single mean, comparing two means, and testing a claim about population characteristics using sample data and statistics.
Testing of Hypothesis combined with tests.pdf
This document discusses hypothesis testing procedures. It defines a hypothesis as a statement about a population parameter that can be tested. The key points covered are:
- Null and alternative hypotheses are defined, with the null hypothesis containing "=", "<", or ">" and the alternative containing "≠", "<", or ">"
- Tests can be one-tailed or two-tailed depending on the alternative hypothesis
- The level of significance and critical values are used to determine whether to reject or fail to reject the null hypothesis
- Type I and type II errors are explained as incorrect rejections or failures to reject the null hypothesis
- Parametric and non-parametric tests are compared based on their data
STATISTIC ESTIMATION
This document provides an overview of statistical inference. It discusses descriptive statistics, which summarize data, and inferential statistics, which are used to generalize from samples to populations. Key concepts covered include estimation, hypothesis testing, parameters, statistics, confidence intervals, significance levels, types of errors. Examples are given of how to calculate confidence intervals for means and proportions and how to perform hypothesis tests using z-tests and t-tests. Steps for conducting hypothesis tests are outlined.
312320.pptx
The document discusses hypothesis testing and outlines the key steps in the hypothesis testing process:
1) Formulating the null and alternative hypotheses about a population parameter. The null hypothesis is tested while the alternative is accepted if the null is rejected.
2) Determining the significance level and critical value based on this level which establishes the boundary for rejecting the null hypothesis.
3) Selecting a sample, calculating the test statistic and comparing it to the critical value to determine whether to reject or fail to reject the null hypothesis.
4) Hypothesis tests can be one-tailed, focusing rejection in one tail, or two-tailed, splitting rejection between both tails. Steps are generally the same but null and alternatives differ.
Review Z Test Ci 1
1. The document discusses hypothesis testing using the z-test. It outlines the steps of hypothesis testing including stating hypotheses, setting the criterion, computing test statistics, comparing to the criterion, and making a decision.
2. Examples are provided to demonstrate a non-directional and directional z-test, including stating hypotheses, computing test statistics, comparing to criteria, and interpreting results.
3. Key concepts reviewed are the central limit theorem, type I and II errors, significance levels, rejection regions, p-values, and confidence intervals in hypothesis testing.
Z-test
This document discusses the Z-test, a statistical test used to compare means and proportions. The Z-test can be used to test if a sample mean differs from a population mean, if two sample means are equal, or if two population proportions are equal. It assumes the population is normally distributed. The steps involve formulating hypotheses, choosing a significance level, calculating the Z-statistic, and comparing it to a critical value to determine if the null hypothesis should be rejected or accepted. The Z-test is useful when sample sizes are large but requires knowing the population standard deviation.
hypothesis test
This document provides an overview of estimation and hypothesis testing. It defines key statistical concepts like population and sample, parameters and estimates, and introduces the two main methods in inferential statistics - estimation and hypothesis testing.
It explains that hypothesis testing involves setting a null hypothesis (H0) and an alternative hypothesis (Ha), calculating a test statistic, determining a p-value, and making a decision to accept or reject the null hypothesis based on the p-value and significance level. The four main steps of hypothesis testing are outlined as setting hypotheses, calculating a test statistic, determining the p-value, and making a conclusion.
Examples are provided to demonstrate left-tailed, right-tailed, and two-tailed hypothesis tests
Day-2_Presentation for SPSS parametric workshop.pptx
This document provides an overview of parametric statistical tests, including t-tests and analysis of variance (ANOVA). It discusses the concepts of statistical inference, hypothesis testing, null and alternative hypotheses, types of errors, critical regions, p-values, assumptions of t-tests, and procedures for one-sample t-tests, independent and paired t-tests, one-way ANOVA, and repeated measures ANOVA. The document is intended as part of an online workshop on using SPSS for advanced statistical data analysis.
Statistical-Tests-and-Hypothesis-Testing.pptx
Here are the steps to solve this hypothesis testing problem:
1. State the null and alternative hypotheses:
H0: There is no significant difference between the means under stress and no stress conditions.
H1: There is a significant difference between the means under stress and no stress conditions.
2. Choose the level of significance: Given as α = 0.01
3. Select the appropriate statistical test: Since this involves comparing the means of two independent groups, use a two-sample t-test.
4. Compute the test statistic and p-value: Follow the t-test formula and calculation.
5. Make a decision: Reject H0 if p-value < α, fail to reject H0 if
Hypothesis Testing Definitions A statistical hypothesi.docx
Hypothesis Testing
Definitions:
A statistical hypothesis is a guess about a population parameter. The guess may or not be
true.
The null hypothesis, written H0, is a statistical hypothesis that states that there is no
difference between a parameter and a specific value, or that there is no difference between
two parameters.
The alternative hypothesis, written H1 or HA, is a statistical hypothesis that specifies a
specific difference between a parameter and a specific value, or that there is a difference
between two parameters.
Example 1:
A medical researcher is interested in finding out whether a new medication will have
undesirable side effects. She is particularly concerned with the pulse rate of patients who
take the medication. The research question is, will the pulse rate increase, decrease, or
remain the same after a patient takes the medication?
Since the researcher knows that the mean pulse rate for the population under study is 82
beats per minute, the hypotheses for this study are:
H0: µ = 82
HA: µ ≠ 82
The null hypothesis specifies that the mean will remain unchanged and the alternative
hypothesis states that it will be different. This test is called a two-tailed test since the
possible side effects could be to raise or lower the pulse rate. Notice that this is a non
directional hypothesis. The rejection region lies in both tails. We divide the alpha in two
and place half in each tail.
Example 2:
An entrepreneur invents an additive to increase the life of an automobile battery. If the
mean lifetime of the automobile battery is 36 months, then his hypotheses are:
H0: µ ≤ 36
HA: µ > 36
Here, the entrepreneur is only interested in increasing the lifetime of the batteries, so his
alternative hypothesis is that the mean is greater than 36 months. The null hypothesis is
that the mean is less than or equal to 36 months. This test is one-tailed since the interest
is only in an increased lifetime. Notice that the direction of the inequality in the alternate
hypothesis points to the right, same as the area of the curve that forms the rejection
region.
Example 3:
A landlord who wants to lower heating bills in a large apartment complex is considering
using a new type of insulation. If the current average of the monthly heating bills is $78,
his hypotheses about heating costs with the new insulation are:
H0: µ ≥ 78
HA: µ < 78
This test is also a one-tailed test since the landlord is interested only in lowering heating
costs. Notice that the direction of the inequality in the alternate hypothesis points to the
left, same as the area of the curve that forms the rejection region.
Study Design:
After stating the hypotheses, the researcher’s next step is to design the study. In designing
the study, the researcher selects an appropriate statistical test, chooses a level of
significance, and formulates a plan for conducting the study..
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Himani
- 14. F-TEST
- 19. XYZ constructions is a leading company in the construction sector in Delhi . It wants to construct flats in two areas, Indrapuram & Pritampura . The company wants to estimate the amount that customers are willing to spend on purchasing a flat in the two areas . It randomly selected 21 potential customers from Pritampura and 27 from Indrapuram and posed the question, “how much are you willing to spend on a flat?” The data collected from the two areas is shown in table below.
- 20. The company assumes that the intention to purchase of the customers is normally distributed with equal variance in the two areas taken for the study. On the basis of the samples taken for the study, estimate the difference in population means taking 95% as the confidence level.
- 21. Proposed Exp. On flats by customers from Indrapuram (in thousand Rs.) 125 165 130 170 126 130 127 145 150 130 135 140 140 150 160 160 120 140 150 145 155 165 145 140 165 135 130 140 145 160 155 150 145 160 155 150 170 160 190 145 180 190 170 180 160 185 165 135 185 Proposed Exp. On flats by customers from Pritampura (in thousand Rs.)