Discuss the below:
Confidence intervals/One sample hypothesis tests
Q1: Calculate and interpret the confidence interval. Please show your manual calculation or the software output. Please show your work if you calculated manually on 1. If you used statistical software, please show the output.
1: Confidence Intervals for the mean:
A researcher is studying stress among executives. The researcher is using a questionnaire that measures stress. The questionnaire has been validated through past use. A score above 80 indicates stress at a dangerous level. A random sample of 15 executives revealed the following stress level scores.
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94
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88
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73
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90
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68
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79
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87
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95
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87
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92
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83
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94
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82
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85
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84
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What is the 95% confidence level? Do you conclude that the executives have a dangerous level of stress? Why?
Q2: Which is a one-sample test, identify the null and alternative hypothesis, and the critical value. Then, calculate or identify the test statistic, and make a decision on the null hypothesis. Explain why you made your decision on the null hypothesis
2: Hypothesis test for the population mean: t test
An electronics manufacturing process has a scheduled mean completion time of 70 minutes. It is claimed that, under new management, the mean completion time μ is less than 70 minutes. To test this claim, a random sample of 13 completion times under new management was taken.
The sample had a mean completion time of 66 minutes and a standard deviation of 10 minutes. Assume that the population of completion times under new management is normally distributed. At the level of significance,0.05 can it be concluded that the mean completion time μ under new management is less than the scheduled mean?
Perform a one-tailed test.
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Hypothesis Test: Mean vs. Hypothesized Value
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70.00
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hypothesized value
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66.00
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mean Q1
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10.00
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std. dev.
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2.77
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std. error
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13
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n
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12
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df
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-1.44
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t
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.0874
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p-value (one-tailed, lower)
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59.96
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confidence interval 95.% lower
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72.04
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confidence interval 95.% upper
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6.04
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half-width
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1: State the null & alternative hypothesis:
2: Identify the critical value
3: Identify the test statistic
4: State and explain your decision on H0
Q3: Which is a one-sample test, identify the null and alternative hypothesis, and the critical value. Then, calculate or identify the test statistic, and make a decision on the null hypothesis. Explain why you made your decision on the null hypothesis
3: Hypothesis test for a population proportion
The manufacturer of a new antidepressant claims that, among all people with depression who use the drug, the proportion Ρ of people who find relief from depression is at least 80%. A random sample of 230 patients who use this new drug is selected, and 178of them find relief from depression. Based on these data, can we reject the manufacturer's claim at the 0.1 level of significance?
Perform a one-tailed test.
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Hypothesis test for proportion vs hypothesized value
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Observed
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Hypothesized
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0.7739
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0.8
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p (as decimal)
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178/230
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184/230
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p (as fraction)
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178.
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184.
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X
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230
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230
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n
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0.0264
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std. error
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-0.99
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z
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.8387
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p-value (one-tailed, upper)
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1: State the null & alternative hypothesis:
2: Identify the critical value
3: Identify the test statistic
4: State and explain your decision on H0