A snack company claims that at least 70% of people prefer its new low-sugar granola bar over the original version. To test this claim, a grocery chain surveys a random sample of 80 customers, & 50 say they prefer the new version. Use $\alpha =0.10$ to test whether more than 70% of customers prefer the new granola bar. Should the grocery chain stock more of the new product & reduce shelf space for the original version?

• A. Yes
• B. No

Answer: (B)

Verified step by step guidance

1. Step 1: Define the null hypothesis (H₀) and the alternative hypothesis (Hₐ). The null hypothesis is H₀: p ≤ 0.70, which states that 70% or fewer customers prefer the new granola bar. The alternative hypothesis is Hₐ: p > 0.70, which states that more than 70% of customers prefer the new granola bar.
2. Step 2: Identify the significance level (α) and the sample statistics. The significance level is given as α = 0.10. The sample size (n) is 80, and the number of customers who prefer the new granola bar is 50. Calculate the sample proportion (p̂) using the formula p̂ = x / n, where x is the number of successes.
3. Step 3: Calculate the test statistic using the formula for a one-proportion z-test: z = (p̂ - p₀) / √(p₀(1 - p₀) / n), where p₀ is the hypothesized population proportion (0.70), p̂ is the sample proportion, and n is the sample size.
4. Step 4: Determine the critical value for a one-tailed test at α = 0.10. Use a z-table or statistical software to find the z-critical value corresponding to a right-tailed test with a significance level of 0.10.
5. Step 5: Compare the calculated z-test statistic to the critical value. If the z-test statistic is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis. Based on the conclusion, decide whether the grocery chain should stock more of the new product or maintain the current shelf space allocation.