Population when the \u03c3 is Known Example Soda Bottles 2 Step 5 Determine whether

Population when the σ is known example soda bottles

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Population when the σ is Known Example: Soda Bottles 2 Step 5: Determine whether to reject H 0 p ≤ α , which means there is little evidence supporting the H 0 . So, we reject the null hypotheses
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Testing a Hypothesis about a Population when the σ is Unknown If we don’t know the population standard deviation ( σ ) we use a t- test. t-test is also very simple: t = ҧ𝑥− 𝜇 0 𝑠/√𝑛 X-bar: sample mean μ 0 : hypothesized population mean s: sample standard deviation n: sample size
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Testing a Hypothesis about a Population when the σ is Unknown Example: Customer Satisfaction A restaurant manager wants to know if customers are happy with the services provided by the restaurant. To do so, they decide to ask customers to rate their overall satisfaction with the restaurant on a scale of 1 to 7. The manager will decide that they are doing fine if the average score is not less than 5. A group of 64 randomly selected consumers are asked to rate their overall satisfaction with the restaurant on a scale of 1 to 7. The average satisfaction rating was 4.91 with a sample standard deviation of 1.34. The restaurant manager wants to perform a hypothesis test, with a .05 level of significance, to determine if the average satisfaction rating is not significantly less than 5.
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Testing a Hypothesis about a Population when the σ is Unknown Example: Customer Satisfaction Step 1: Develop the hypotheses H 0 : μ 5 H a : μ < 5 Step 2: Determine the level of significance α = 0.05
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Testing a Hypothesis about a Population when the σ is Unknown Example: Customer Satisfaction Step 3: Compute the test statistic t = ҧ𝑥− 𝜇 0 𝑠/√𝑛 = = 4.91−5 1.34/√64 = -0.54 Step 4: Compute the p-value 0 t .05 = -1.669 -.54 p-value > .20
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Testing a Hypothesis about a Population when the σ is Unknown Example: Customer Satisfaction Step 5: Determine whether to reject H 0 p > α , which means we cannot reject the null hypothesis
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