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How to Determine a p-Value When Testing a Null Hypothesis

Null and Alternative Hypotheses for a Mean

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Support or Reject Null Hypothesis

As described in the topic on if p With ANOVA, if the null hypothesis is rejected, then all we know is that at least 2 groups are different from each other.

Click the link the skip to the situation you need to support or reject null hypothesis for:

The p-value tells you how unlikely this sample (ora more extreme one) is if the null hypothesis is true. The moreunlikely (surprising, unexpected), the lower the p-value, and the more confident you can feelabout rejecting H0.

State the Null Hypothesis and the Alternative Hypothesis.

1. If p is less than or equal to alpha, then reject the nullhypothesis

where the observed sample mean, μ0 = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences.

When you about a , you can use your test statistic to decide whether to reject the null hypothesis, H0. You make this decision by coming up with a number, called a -value.

Based from this problem, the appropriate null hypothesis will

2. If p is greater than alpha, the fail to reject the null hypothesis.

A related criticism is that a significant rejection of a null hypothesis might not be biologically meaningful, if the difference is too small to matter. For example, in the chicken-sex experiment, having a treatment that produced 49.9% male chicks might be significantly different from 50%, but it wouldn't be enough to make farmers want to buy your treatment. These critics say you should estimate the effect size and put a on it, not estimate a P value. So the goal of your chicken-sex experiment should not be to say "Chocolate gives a proportion of males that is significantly less than 50% (P=0.015)" but to say "Chocolate produced 36.1% males with a 95% confidence interval of 25.9 to 47.4%." For the chicken-feet experiment, you would say something like "The difference between males and females in mean foot size is 2.45 mm, with a confidence interval on the difference of ±1.98 mm."

Back in Chapter 8, you learned the CLT’s:random sample not larger than 10% of population,and at least 10 successes and 10 failures expectedif the null hypothesis is true. You compute expected successes aso by using o, which is the number from H0. Expected failures arethen sample size minus expected successes, −o insymbols. need the samplingdistribution of the proportion to be a , so you must check therequirements as part of your hypothesis test.

This is the critical value that we need if we want to reject the null hypothesis.
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  • Remember that in most cases, the null hypothesis is

    The null hypothesis is rejected at the 0.05 level of significance and one star (*) is printed somewhere in a table.

  • On the other extreme, if we reject the null hypothesis if and only if

    If you are able to reject the null hypothesis in Step 2, you can replace it with the alternate hypothesis.

  • Thus, we tend to do not reject the null hypothesis.

    A small p value associated with a sample mean indicates a rare occurrence andwould lead one reject the null hypothesis.

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Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

Example 11: Suppose your null hypothesis is “the average package containsthe stated net weight,” your alternative is “the averagepackage contains less than the stated net weight,” and yoursignificance level α is 0.05.

When we evaluate the nullhypothesis, we can make 2 types of errors.

In a nice phrase,say that p-values “measure the strength of the evidence againstthe null hypothesis; the smaller the p-value, the stronger theevidence against the null hypothesis.” They also quote oninterpreting a p-value:“If P is between 0.1 and 0.9 there is certainly no reason tosuspect the hypothesis tested. If it is below 0.02 it is stronglyindicated that the hypothesis fails to account for the whole of thefacts. We shall not often be astray if we draw a conventional line at0.05.”

Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

If the p-value is small, your results are in conflict withH0, so you reject the null and accept the alternative. If thep-value is larger, your sample is not in conflict with H0 and youfail to reject the null, which is stats-talk for failing to reach anykind of conclusion.

The P value is NOT the probability that the null hypothesis is true.

To answer that you need to identify your nullhypothesis H0. Remember that it’s always some form of“nothing going on here.” In this case, H0 would be thatthe defendant didn’t commit the murder, and H1 would be thathe did.

the null hypothesis is rejected when it is true b.

Example 4: Suppose your alternative hypothesis H1 is that a newheadache remedy PainX helps a greater proportion of people thanaspirin.

the null hypothesis is not rejected when it is false c.

The P value for testing the null hypothesis that the coin is fair (equally likely to come up heads or tails) versus the alternative that is it unfair is 0.0035.

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