Hypothesis Testing: Suppose a PM claims that users, on average, spend about $50 per month on Amazon. However, you doubt this claim and believe the average should be higher. You sample 100 users and find the sample mean is $85. Would you reject the PM's claim? Assume population standard deviation is 20.

Yes, I would reject the PM's claim. We can perform a one-sample z-test since the sample size (n=100) is large and the population standard deviation (σ=20) is known. The null hypothesis is that the average monthly spending is $50 (μ = 50), and the alternative hypothesis is that it is greater than $50 (μ > 50). The sample mean is $85 (x̄ = 85). The calculated z-score is (85 - 50) / (20 / √100) = 35 / 2 = 17.5. This extremely high z-score corresponds to a p-value very close to zero. Since this p-value is significantly less than any conventional significance level (e.g., 0.05), we reject the null hypothesis and conclude that the average monthly spending is indeed higher than $50.