Question

Decide whether the normal sampling distribution can be used It a can be used, tost the daim about the population propertion pat the given ierel of sigrificance a using the given sample statiatics Clain.p 2024.α=0.05. Sample Matistics. p^​=022,n=200 Can the normal samping datribution be usod? A. No, because np is less than 5 11. Yes, because pq is greater than α=0.05 No, because ng is less than 5 10. Yes, because both ne and oq are greater than or equal to 5 State the moll and alternatie hypotheses. A H3​p=0.24 Ha​,p×024 त. H0​p⩽024 Ha​p>024 C. H0​⋅p2024 H0​,p<024 D. The tost cannot be performed Determine the critical value(s). Select the correct choice below and, it necessary, fal in the answer box to complete your choice. A. The cribcal value(s) tiare (Round to two decimal places as needed Use a commu to separate answem as needed.) 8. The test cannot be performed

Answer 1

Using the given sample statistics, the normal sampling distribution can be used because both np and nq are greater than 5. The null and alternative hypotheses are H₀: p = 0.24 and H₁: p ≠ 0.24 respectively. The critical z-values for α = 0.05 in a two-tailed test are ±1.96.

Step-by-step explanation:

To determine if we can use the normal sampling distribution for testing the claim about the population proportion, we should check if np and nq are both greater than or equal to 5.

Given the sample statistics, with p = 0.22 and n = 200, we calculate np = 0.22 * 200 = 44 and nq = (1-0.22) * 200 = 0.78 * 200 = 156. Since both values are greater than 5, the normal sampling distribution can be used.

The null and alternative hypotheses for testing the claim that p = 0.24 at the 0.05 level of significance are as follows:

• H₀: p = 0.24
• H₁: p ≠ 0.24

For a two-tailed test using the normal distribution, we need to calculate the critical value(s). Since the level of significance is α = 0.05, the critical z-values will be ±1.96.