One Sample Test 15 Ptsa The Owner Of A Local Nightclub

Question

One Sample Test 15 Ptsa The Owner Of A Local Nightclub Has Rec One Sample Test 15 Ptsa The Owner Of A Local Nightclub Has Rec The owner of a local nightclub conducted a survey with a random sample of 250 customers to determine if the mean age exceeds 30 years. The sample mean age was found to be 30.45 years with a standard deviation of 5 years. The owner wishes to be 99% confident in her decision to assess whether the average customer age is over 30, which informs her planned entertainment adjustments. Additionally, a major DVD rental chain is contemplating opening a new store in an area without existing stores. To decide, they survey 300 households and find that 96 have DVD players, thus testing whether more than 5,000 of 20,000 households are equipped with DVD players.

Dr. Jack HW Helper · Accepted Answer

Introduction Statistical hypothesis testing provides a key tool to inform business and community decisions. Whether assessing customer demographics or evaluating new market locations, accurate interpretation of sample data is essential. In this paper, we analyze the two scenarios: the nightclub owner's inquiry into customer age demographics and the DVD rental chain's investigation of market readiness based on household DVD player ownership. Case 1: Nightclub Customer Age Analysis The nightclub owner’s primary question concerns whether the average age of her clientele exceeds 30 years. The sample data includes a sample mean ($\bar{x}$) of 30.45 years, a standard deviation (s) of 5 years, and a sample size (n) of 250. The hypotheses are formulated as follows: Null hypothesis ($H_0$): $\mu \leq 30$ years Alternative hypothesis ($H_1$): $\mu > 30$ years Given the sample data, the test statistic is calculated using the one-sample z-test for mean, because the population standard deviation is estimated from the sample: $$ z = \frac{\bar{x} - \mu_0}{s / \sqrt{n}} = \frac{30.45 - 30}{5 / \sqrt{250}} \approx \frac{0.45}{0.316} \approx 1.42 $$ Using a standard normal distribution table, the critical z-value for a 99% confidence level (significance level $\alpha = 0.01$) in a one-tailed test is approximately 2.33. Since 1.42 Therefore, there is not enough statistical evidence to conclude that the mean age of customers exceeds 30 years. The owner may decide to retain current entertainment plans, as the data suggests the average customer age is likely around 30 or below. Case 2: Market Readiness for DVD Store The DVD rental chain's interest is in whether the proportion of households in the area owning DVD players exceeds 5,000 out of 20,000 households, which equates to 25%. The sample data shows 96 households with DVD players out of 300 surveyed, representing an observed proportion ($\hat{p}$) of: $$ \hat{p} = \frac{96}{300} = 0.32 $$ The hypotheses for this test

One Sample Test 15 Ptsa The Owner Of A Local Nightclub

One Sample Test 15 Ptsa The Owner Of A Local Nightclub Has Rec

Sample Paper For Above instruction

Introduction

Case 1: Nightclub Customer Age Analysis

Case 2: Market Readiness for DVD Store

Conclusion

References