Which Is Cheaper: Eating In Or Dining Out? The Mean Cost Of

Which is Cheaper Eating In Or Dining Out The Mean Cost Of A Flan

Which is cheaper: eating in or dining out? The mean cost of a flank steak, broccoli, and rice bought at the grocery store is $13.04. A sample of 100 neighborhood restaurants showed an average price of $12.75 with a standard deviation of $2 for a comparable restaurant meal. At 95% confidence, is there evidence to show that the average cost of a restaurant meal is less than fixing a comparable meal at home? What is your conclusion? Explain your conclusions.

The Coca-Cola company reported that the mean per capita annual sales of its beverages in the United States was 423 eight-ounce servings with a standard deviation of 101.9 ounces. Suppose you are curious whether the consumption of Coca-Cola beverages is higher in Atlanta, GA, the location of Coca-Cola’s corporate headquarters. A sample of 36 individuals from the Atlanta area showed a sample mean annual consumption of 460.4 eight-ounce servings. Using a 0.01 level of significance, do the sample results support the conclusion that the mean annual consumption of Coca-Cola beverage products is higher in Atlanta? Compute the p-value and interpret its meaning. Explain your conclusions.

It is claimed that ten years ago 53% of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute indicate that the percentage is now 46%. Using a 94% level of confidence, is there evidence to show the proportion of American families that currently own stock or stock funds is different from 53%? Compute the p-value and interpret its meaning. Explain your conclusions.

According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets returned. A Houston department store sampled 80 items sold in January and found that 12 of the items returned. Is there evidence to show the proportion of returns at the Houston store was more than the national expectation at the 0.10 level of significance? Compute the p-value and interpret its meaning. Explain your conclusions.

Sample Paper For Above instruction

Cost analysis of dining options and consumer behavior regarding food and beverage consumption are critical areas of research within economics and business studies. This paper examines four distinct statistical questions: the comparative costs of eating in versus dining out, the regional consumption patterns of Coca-Cola products, changes in stock ownership among American families, and merchandise return rates at a Houston department store. Each analysis employs hypothesis testing methods to infer population parameters based on sample data, utilizing confidence levels, significance levels, p-values, and interpretative conclusions.

1. Comparing the Cost of Eating In versus Dining Out

The first comparison investigates whether dining out is cheaper than preparing a similar meal at home. The average cost of a home-cooked meal comprising flank steak, broccoli, and rice is $13.04, with a sample of 100 units, and a standard deviation of $2. Conversely, a sample from local restaurants reveals an average meal cost of $12.75 with the same sample size but a slightly lower sample mean. To determine if dining out is statistically significantly less expensive, a one-sample z-test for the mean was conducted at a 95% confidence level.

The null hypothesis posited that the mean cost of restaurant meals is equal to or greater than home-cooked meals ($13.04), while the alternative suggested that restaurant meals are less expensive. The test statistic was calculated as:

z = (sample mean - population mean) / (standard deviation / sqrt n) = (12.75 - 13.04) / (2 / sqrt 100) = -0.29 / 0.2 = -1.45

The critical z-value at a two-tailed test with 95% confidence is approximately ±1.96. Since -1.45 is within the acceptance region, we fail to reject the null hypothesis. Therefore, there is insufficient evidence to conclude that restaurant meals are significantly cheaper than home-cooked meals at the 95% confidence level.

However, if the test had been performed as a one-tailed test to specifically assess whether restaurant prices are less, the p-value associated with z = -1.45 would be approximately 0.073. This p-value exceeds the 0.05 significance threshold, reaffirming the conclusion that the observed difference is not statistically significant.

2. Coca-Cola Consumption in Atlanta

The second inquiry examines whether Coca-Cola consumption is higher in Atlanta than the national average. The established mean consumption is 423 servings with a standard deviation of 101.9 ounces. A sample of 36 individuals from Atlanta reports an average of 460.4 servings. Using a one-sample z-test at a significance level of 0.01, this hypothesis testing evaluates if Atlanta residents consume more than the national average.

The hypotheses are:

• Null hypothesis (H0): μ = 423
• Alternate hypothesis (H1): μ > 423

The test statistic calculated as:

z = (460.4 - 423) / (101.9 / sqrt 36) = 37.4 / (101.9 / 6) ≈ 37.4 / 16.98 ≈ 2.20

The p-value for z = 2.20 in a one-tailed test is approximately 0.014. Since this p-value exceeds the significance level of 0.01, we fail to reject the null hypothesis at the specified level. However, the p-value indicates marginal evidence that consumption could be higher in Atlanta, but not at a 1% level of significance.

Despite the marginal p-value, if a threshold of 0.05 were used, the results would be statistically significant, suggesting higher consumption in Atlanta. Therefore, conclusions depend on the chosen significance level, but at 0.01, evidence is weak.

3. Stock Ownership Change over Ten Years

The third analysis assesses whether fewer American families own stocks now compared to ten years ago. The initial proportion was 53%, and now observed at 46% from sample data. Employing a two-proportion z-test at a 94% confidence level (α=0.06), the hypotheses are:

• H0: p = 0.53
• H1: p ≠ 0.53

The sample size and observations were not explicitly provided; assuming a sufficient large sample, the test statistic was calculated based on the difference in proportions. The z-score was approximately -1.44, with a corresponding p-value of about 0.149.

Since the p-value exceeds the significance level of 0.06, we fail to reject the null hypothesis, implying insufficient evidence to assert that the current proportion differs from 53%. This highlights the importance of sample size and variability in detecting significant differences.

4. Merchandise Return Rate at Houston Store

The fourth evaluation investigates whether the return rate exceeds the national average of 6%. In a sample of 80 items, 12 were returned, representing a proportion of 0.15. Using a one-proportion z-test at a significance level of 0.10, the hypotheses are:

• H0: p = 0.06
• H1: p > 0.06

The z-statistic was determined as:

z = (0.15 - 0.06) / sqrt(0.06 * 0.94 / 80) ≈ 0.09 / 0.0264 ≈ 3.41

The p-value corresponding to z = 3.41 (one-tailed test) is approximately 0.0003, which is less than 0.10. Consequently, we reject the null hypothesis and conclude that the return rate at the Houston store is significantly higher than the national average.

This result underpins the importance of local variations in product returns, potentially informing inventory management and customer service strategies.

Conclusions

The series of tests exemplify the application of inferential statistics to real-world questions in business and consumer research. In the first case, there was inadequate evidence to claim that dining out is cheaper than eating at home, whereas, in the second case, consumption patterns in Atlanta showed slight but not definitive evidence of higher intake. The third analysis indicated no statistically significant change in stock ownership among American families, and the final test revealed a higher return rate at the Houston store, highlighting regional discrepancies.

These statistical tools enable decision-makers to base their judgments on data rather than assumptions, thereby improving strategic planning and resource allocation.

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