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# Confidence Intervals for mean; t test; hypothesis test for proportion

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Confidence intervals/One sample hypothesis tests

Directions: For #1, 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.
94
88
73
90
68
79
87
95
87
92
83
94
82
85
84

What is the 95% confidence level? Do you conclude that the executives have a dangerous level of stress? Why?

For #2, 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 minutes. It is claimed that, under new management, the mean completion time, , is less than minutes. To test this claim, a random sample of completion times under new management was taken.
The sample had a mean completion time of minutes and a standard deviation of minutes. Assume that the population of completion times under new management is normally distributed. At the level of significance, can it be concluded that the mean completion time, , under new management is less than the scheduled mean?
Perform a one-tailed test.
Hypothesis Test: Mean vs. Hypothesized Value

70.00 hypothesized value
66.00 mean Q1
10.00 std. dev.
2.77 std. error
13 n
12 df

-1.44 t
.0874 p-value (one-tailed, lower)

59.96 confidence interval 95.% lower
72.04 confidence interval 95.% upper
6.04 half-width
1: State the null & alternative hypothesis:
2: Identify the critical value
3: Identify the test statistic
4: State and explain your decision on H0
For #3, 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 of people who find relief from depression is at least . A random sample of patients who use this new drug is selected, and of them find relief from depression. Based on these data, can we reject the manufacturer's claim at the level of significance?
Perform a one-tailed test.
Hypothesis test for proportion vs hypothesized value

Observed Hypothesized
0.7739 0.8 p (as decimal)
178/230 184/230 p (as fraction)
178. 184. X
230 230 n

0.0264 std. error
-0.99 z
.8387 p-value (one-tailed, upper)

1: State the null & alternative hypothesis:
2: Identify the critical value
3: Identify the test statistic
4: State and explain your decision on H0

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#### Solution Preview

Confidence intervals/One sample hypothesis tests

Directions: For #1, 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.
94
88
73
90
68
79
87
95
87
92
83
94
82
85
84

What is the 95% confidence level? Do you conclude that the executives have a dangerous level of stress? Why?

The 95% confidence interval is given by the formula
Details

Confidence Interval Estimate for the Mean

Data
Sample Standard Deviation 7.716401826
Sample Mean 85.4
Sample Size 15
Confidence Level 95%

Intermediate Calculations
Standard Error of the Mean 1.992366384
Degrees of Freedom 14
t Value 2.144786681
Interval Half Width 4.273200885

Confidence Interval
Interval Lower Limit 81.13
Interval Upper Limit 89.67

Interpretation: With 95% confidence we can claim that the population mean stress score is ...

#### Solution Summary

The expert determines the confidence intervals for mean, t tests and hypothesis tests for proportions.

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