The table below provides a random sample of 20 exam scores for a large geology class. Use Excel to construct a 90% confidence interval for the mean exam score of the class. Round your answers to one decimal place and use ascending order.Score

91

91

95

96

78

60

61

94

94

80

82

89

99

79

79

87

73

87

96

71

To construct a 90% confidence interval for the mean exam score using Excel, follow these steps:

### Step 1: Input the Data
1. Enter the given data into a column in Excel. For example, enter the data from cell A1 to A20.

### Step 2: Calculate the Mean
1. Use the `AVERAGE` function to calculate the mean (x̄) of the data.
   - Formula: `=AVERAGE(A1:A20)`

### Step 3: Calculate the Sample Standard Deviation
1. Use the `STDEV.S` function to calculate the sample standard deviation (s).
   - Formula: `=STDEV.S(A1:A20)`

### Step 4: Determine the Sample Size (n)
1. The sample size (n) is 20 (as there are 20 scores).

### Step 5: Find the t-Score for the 90% Confidence Level
1. Use the `T.INV.2T` function to find the t-score corresponding to a 90% confidence level.
   - Formula: `=T.INV.2T(0.10, n-1)`
   - In this case: `=T.INV.2T(0.10, 19)`

### Step 6: Calculate the Margin of Error (E)
1. Use the formula \(E = t \times \frac{s}{\sqrt{n}}\) to calculate the margin of error.
   - Formula: `=t * (s / SQRT(n))`

### Step 7: Determine the Confidence Interval
1. Calculate the lower bound of the confidence interval:
   - Formula: `=Mean - E`
2. Calculate the upper bound of the confidence interval:
   - Formula: `=Mean + E`

### Example Calculation in Excel:
Assuming the data is in cells A1 to A20:

1. **Mean (x̄)**: `=AVERAGE(A1:A20)`
2. **Sample Standard Deviation (s)**: `=STDEV.S(A1:A20)`
3. **t-Score for 90% Confidence Level**: `=T.INV.2T(0.10, 19)` (which gives approximately 1.729)
4. **Margin of Error (E)**: `=t * (s / SQRT(20))`
5. **Lower Bound**: `=Mean - E`
6. **Upper Bound**: `=Mean + E`

### Final Calculation:
Let’s use these exact numbers:

1. **Mean**: \( \text{Mean} \approx 83.9 \)
2. **Standard Deviation (s)**: \( \text{s} \approx 11.1 \)
3. **t-Score**: \( \text{t} \approx 1.729 \)
4. **Margin of Error (E)**: \( E \approx 4.3 \)

Finally, the 90% confidence interval is:
\[ (83.9 - 4.3, 83.9 + 4.3) \]

So, the 90% confidence interval for the mean exam score is approximately:
\[ \textbf{(79.6, 88.2)} \]

### Summary:
The 90% confidence interval for the mean exam score is \(\textbf{(79.6, 88.2)}\).

---

Would you like a detailed explanation of any of these steps or help with further questions?

Here are five additional questions you might find interesting:

1. How would the confidence interval change if the sample size were increased to 30?
2. What would be the 95% confidence interval using the same data?
3. How does the confidence interval change if the standard deviation was calculated from a larger sample?
4. Can you determine the required sample size to achieve a margin of error of 2 points with 90% confidence?
5. What is the effect of increasing the confidence level to 95%?

**Tip:** In hypothesis testing, a smaller sample size generally results in a wider confidence interval.

Learn how to construct a 90% confidence interval for the mean exam score using Excel. Includes step-by-step instructions with a sample calculation using a dataset of 20 exam scores. Discover how to calculate the mean, sample standard deviation, t-score, margin of error, and determine the confidence interval.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation