I see you've uploaded an image containing a hypothesis testing problem for a scenario regarding a wilderness trip company's customer survey. I'll help you work through the details step-by-step.

Problem Overview:

• Claim: At least 70% of all customers found the experience "worth the cost."
• Sample: 3,361 customers surveyed, where:
  • 2,017 said "YES" (60%),
  • 1,344 said "NO" (40%).
• Alpha: 20% significance level ($\alpha = 0.20$).
• Test whether the proportion of customers who said "YES" supports the claim that at least 70% of customers are satisfied.

Step-by-Step Solution:

1. Define Hypotheses:

• Null Hypothesis ($H_0$): $p \geq 0.70$ (The population proportion of "YES" is at least 70%.)
• Alternative Hypothesis ($H_a$): $p < 0.70$ (The population proportion of "YES" is less than 70%.)

2. Significance Level:

• $\alpha = 0.20$.

3. Test Type:

• One-tailed (Left-tailed test).

4. Calculate Sample Proportion:

$\hat{p} = \frac{\text{Number of "YES"}}{\text{Total Surveyed}} = \frac{2017}{3361} \approx 0.6004$

5. Standard Error:

The standard error ($SE$) for a proportion is given by: $SE = \sqrt{\frac{p_0 (1 - p_0)}{n}}$ Substituting $p_0 = 0.70$ and $n = 3361$: $SE = \sqrt{\frac{0.70 \cdot 0.30}{3361}} \approx 0.0089$

6. Test Statistic (z):

The z-score formula is: $z = \frac{\hat{p} - p_0}{SE}$ Substituting the values: $z = \frac{0.6004 - 0.70}{0.0089} \approx -11.17$

7. Critical Value (z-critical):

For a left-tailed test with $\alpha = 0.20$:

• $z_{\text{critical}} \approx -0.84$ (from z-tables).

8. Decision Rule:

• Reject $H_0$ if $z$ is less than $z_{\text{critical}}$.

Here, $z = -11.17$ is much smaller than $z_{\text{critical}} = -0.84$.

9. Conclusion:

• Reject $H_0$. There is strong evidence to suggest that less than 70% of all customers believe the experience is worth the cost.

Final Report for Your Template:

• Claim: At least 70% of customers found the experience worth the cost.
• $H_0$: $p \geq 0.70$
• $H_a$: $p < 0.70$
• Alpha ($\alpha$): 0.20
• Tail: Left-tailed test
• Critical Value: $z_{\text{critical}} = -0.84$
• Test Statistic: $z = -11.17$
• Decision: Reject $H_0$
• Conclusion: The data does not support the claim that at least 70% of customers found the experience worth the cost.

Would you like me to fill out specific parts of this worksheet or clarify any part of the process?

Relative Questions:

1. How would the conclusion change if the alpha value was lowered to 0.05?
2. How do you interpret a z-score of -11.17 in the context of this test?
3. What Excel functions could be used to calculate the z-score and critical values automatically?
4. How does increasing the sample size affect the standard error and test outcome?
5. Could this hypothesis test be conducted using a confidence interval approach? If so, how?

Tip: Always visualize the critical region and sample statistics on a normal curve to better understand hypothesis testing outcomes!