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Null and Alternative Hypotheses for a Mean
This is quite simple and is just achieved in a sentence. For this question, we could say something along the lines:
The variable of interest is the score obtained on the standardised test taken in the room with floral scent.
The pvalue is p = 0.019. This is below the .05 standard, so the result is statistically significant. This means we decide in favor of the alternative hypothesis. We're deciding that the population mean is not 72.
To obtain the exact pvalue, use statistical software.
Pulse rates for n = 35 women are available. Here are Minitab results for our hypothesis test. The Minitab process is simply go to Stat > Basic Statistics and select 1Sample t. Select the radio button for Summarized data and enter the values of the sample size, sample mean, and sample standard deviation. Next select the checkbox for Perform Hypothesis Test and enter the hypothesized μ_{o} value. Finally, the default alternative is "not equal". To select a different alternative click Options and select the proper option from the drop down list next to Alternative.
Last week we covered hypothesis tests for possible value of a population proportion (denoted by p). With some adjustments to the details of formulas we can use the same basic steps to carry out hypothesis tests for possible values of a population mean (denoted by the symbol μ).
How to Determine a pValue When Testing a Null Hypothesis
If H_{a} contains a notequalto alternative, find the probability that is beyond your test statistic and double it. There are two cases:
NOTE: The increments for the degrees of freedom in are not always 1. This column increases by 1 up to DF = 30, then the increments change. If your DF is not found in the table just go to the nearest DF. Also, note that the last row, "Infinite", displays the same pvalues as those found in Standard Normal Table. This is because as n increases the tdistribution maps the standard normal distribution.
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To find thevalue for your test statistic:
If H_{a} contains a greaterthan alternative, find the probability that is greater than your test statistic (look up your test statistic on the table, find its corresponding probability, and subtract it from one). The result is yourvalue. (Note: In this case, your test statistic is usually positive.)
Use the following formula to calculate your test value.
Because this is a twosided alternative hypothesis, the pvalue is the combined area to the right of 2.47 and the left of −2.47 in a tdistribution with 35 – 1 = 34 degrees of freedom.
Use the following formula to calculate your test value.
Compare your to α. Support or reject null hypothesis? If the is less, reject the null hypothesis. If the Pvalue is more, keep the null hypothesis.
0.003
the value would be 2 ∗ 0.1056, or 0.2112.
Test statistic: A number, calculated from your data, usually for the purpose of testing H_{0}. It’s often — but not always — calculated as the ratio of a number that measures the size of the effect (the signal) divided by a number that measures the size of the random fluctuations (the noise).
Null and Alternative Hypotheses for a Mean
If your test statistic is negative, first find the probability that is less than your test statistic (look up your test statistic on the table and find its corresponding probability). Then double this probability to get thevalue.
More often than not it is a tvalue.
If H_{a} contains a lessthan alternative, find the probability that is less than your test statistic (that is, look up your test statistic on the table and find its corresponding probability). This is thevalue. (Note: In this case, your test statistic is usually negative.)
How to Determine a pValue When Testing a Null Hypothesis
If your test statistic is positive, first find the probability that is greater than your test statistic (look up your test statistic on the table, find its corresponding probability, and subtract it from one). Then double this result to get thevalue.
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