Question

g According to the U.S. department of Agriculture (USDA), 48.9% of males aged 20 to 39 years consume the recommended daily requirement of calcium. After an aggressive "Got Milk" advertising campaign, the USDA conducts a survey of 35 randomly selected males aged 20 to 39 and finds that 21 of them consume the recommended daily allowance (RDA) of calcium. At the ????=0.05level of significance, is there evidence to conclude that the percentage of males aged 20 to 39 who consume the RDA of calcium has increased?

Answer 1

To determine if there is evidence to conclude that the percentage of males aged 20 to 39 who consume the recommended daily allowance (RDA) of calcium has increased, we can perform a hypothesis test. According to the survey data, the test statistic is not greater than the critical value at the 0.05 level of significance, so we fail to reject the null hypothesis and conclude that there is no evidence of an increase in the percentage of males consuming the RDA of calcium.

Step-by-step explanation:

To determine if there is evidence to conclude that the percentage of males aged 20 to 39 who consume the recommended daily allowance (RDA) of calcium has increased, we can perform a hypothesis test.

Step 1: Formulate the hypotheses

• Null Hypothesis (H0): The percentage of males who consume the RDA of calcium has not increased.
• Alternative Hypothesis (Ha): The percentage of males who consume the RDA of calcium has increased.

Step 2: Set the level of significance (α)

In this case, the level of significance (α) is 0.05.

Step 3: Collect and analyze the data

According to the U.S. department of Agriculture (USDA), the percentage of males aged 20 to 39 who consume the RDA of calcium is 48.9%. After the advertising campaign, a survey of 35 randomly selected males aged 20 to 39 found that 21 of them consume the RDA of calcium.

Step 4: Perform the hypothesis test

1. Calculate the test statistic:
2. Under the null hypothesis, the test statistic follows a binomial distribution with n = 35 and p = 0.489.
3. Calculate the test statistic using the formula: test statistic = (x - np) / sqrt(np(1-p)), where x is the number of males who consume the RDA of calcium.
4. Using the given values, the test statistic is: (21 - (35)(0.489)) / sqrt((35)(0.489)(1-0.489)) = 0.853.
5. Calculate the critical value:
6. Since the test statistic follows a normal distribution under large sample sizes, we can use the z-score to find the critical value.
7. Using a significance level of 0.05, the critical value is 1.645.
8. Make a decision:
9. If the test statistic is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
10. In this case, the test statistic (0.853) is not greater than the critical value (1.645).

Step 5: Draw a conclusion

Since the test statistic is not greater than the critical value at the 0.05 level of significance, we fail to reject the null hypothesis. Therefore, there is no evidence to conclude that the percentage of males aged 20 to 39 who consume the RDA of calcium has increased.

Answer 2

We can conclude that there is no sufficient evidence to conclude that the percentage of males aged 20 to 39 who consume the RDA of calcium has increased

Step-by-step explanation:

H0 : p = 0.489

H1 : p > 0.489

Phat = x/ n ; x = 21 ; n = 35

Phat = x/ n = 21 / 35 = 0.6

Test statistic :

(Phat - P0) ÷ sqrt[P0(1 - P0) /n]

1 - P0 = 1 - 0.489 = 0.511

Phat - P0 = 0.6 - 0.489 = 0.111

Test statistic = 0.111 ÷ sqrt[(0.489 * 0.511) / 35]

Test statistic = 0.111 ÷ sqrt(0.0071394)

Test statistic = 0.111 ÷ 0.0844949

Test statistic = 1.314

Pvalue from Tstatistic :

Pvalue = P(Z < 1.314) = 0.90558

α = 0.05

Pvalue > α ; Hence, we fail to reject the Null

We can conclude that there is no sufficient evidence to conclude that the percentage of males aged 20 to 39 who consume the RDA of calcium has increased