Question 1197932
**1. Define Hypotheses**

* **Null Hypothesis (H0):** The number of HDTVs per household in Boise follows a normal distribution with a mean of 2.30 and a standard deviation of 1.474.
* **Alternative Hypothesis (H1):** The number of HDTVs per household in Boise does not follow a normal distribution.

**2. Determine Expected Frequencies**

* **Divide the data into intervals:** 
    * 0.5 - 1.5
    * 1.5 - 2.5
    * 2.5 - 3.5
    * 3.5 - 4.5
    * 4.5 - 5.5
    * 5.5 and above

* **Calculate the z-scores for the interval boundaries:**
    * For example, for the first interval (0.5 - 1.5):
        * z1 = (0.5 - 2.30) / 1.474 = -1.22
        * z2 = (1.5 - 2.30) / 1.474 = -0.54

* **Use the standard normal distribution table (z-table) to find the area under the curve for each interval.**
* **Multiply the area under the curve for each interval by the sample size (100) to get the expected frequency for that interval.**

**3. Calculate the Chi-Square Test Statistic**

* **For each interval:**
    * Calculate the difference between the observed frequency and the expected frequency.
    * Square the difference.
    * Divide the squared difference by the expected frequency.
* **Sum the values calculated for each interval.** This sum is the chi-square test statistic.

**4. Determine the Degrees of Freedom**

* Degrees of freedom (df) = k - p - 1 
    * where k is the number of intervals (6 in this case)
    * and p is the number of parameters estimated from the sample (0 in this case, as we are using the population mean and standard deviation)
    * df = 6 - 0 - 1 = 5

**5. Find the Critical Value**

* Use a chi-square distribution table to find the critical value at the 0.05 significance level with 5 degrees of freedom.

**6. Compare the Test Statistic to the Critical Value**

* If the calculated chi-square test statistic is greater than the critical value, reject the null hypothesis. 
* If the calculated chi-square test statistic is less than or equal to the critical value, fail to reject the null hypothesis.

**7. Conclusion**

* If you reject the null hypothesis, you can conclude that the number of HDTVs per household in Boise does not follow a normal distribution.
* If you fail to reject the null hypothesis, you cannot conclude that the number of HDTVs per household in Boise does not follow a normal distribution.

**Note:**

* This is a general outline of the process. You would need to use statistical software or a calculator to perform the calculations and find the critical value.
* This analysis assumes that the sample is representative of the population of households in Boise.

**Disclaimer:** This explanation provides a general framework. The specific calculations and interpretations may vary depending on the software used and the exact values obtained.