15. The government claims that the monthly expenses of a Filipino family with four members is P10,000. A sample of 26 family’s expenses has a mean of P10,900 and a standard deviation of P1,250. Is there enough evidence to reject the government’s claim at 𝛼 = 0. 01 How can you find the computed test value?i. Identify the given ii. Use the formula for t-test iii. Substitute the given value to the formula. iv. Solve for the computed t-value.*A. I, ii, iii, ivB. i, ii, iiiC. iv onlyD. I, iii , ii, iv
Question
15. The government claims that the monthly expenses of a Filipino family with four members is P10,000. A sample of 26 family’s expenses has a mean of P10,900 and a standard deviation of P1,250. Is there enough evidence to reject the government’s claim at 𝛼 = 0. 01 How can you find the computed test value?i. Identify the given ii. Use the formula for t-test iii. Substitute the given value to the formula. iv. Solve for the computed t-value.*A. I, ii, iii, ivB. i, ii, iiiC. iv onlyD. I, iii , ii, iv
Solution
The correct answer is A. I, ii, iii, iv.
Here's how you can find the computed test value:
i. Identify the given:
- The government's claim (population mean, μ) = P10,000
- Sample mean (x̄) = P10,900
- Sample standard deviation (s) = P1,250
- Sample size (n) = 26
- Significance level (α) = 0.01
ii. Use the formula for t-test: The formula for a one-sample t-test is t = (x̄ - μ) / (s/√n)
iii. Substitute the given value to the formula: t = (P10,900 - P10,000) / (P1,250/√26)
iv. Solve for the computed t-value: Plug the values into the formula and calculate the t-value. This will be your computed test value.
Remember, if the computed t-value is greater than the critical t-value (which you can find in a t-distribution table), then there is enough evidence to reject the government's claim.
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