EXERCISE 3
Directions: Identify the appropriate test statistic for each of the following, then justify your answer. (2 points each)
1. It is believed that the average monthly salary of a blogger is at least Php 100 000. A random sample of ten bloggers has shown an average monthly salary of Php 112 000 with a standard deviation of Php 15 000. At 0.01 level of significance, is the hypothesized mean true?
2. A new established restaurant in the city claims that the waiting time for customers is less than 15 minutes with a standard deviation of 2.5 minutes. Fifty randomly selected customers have reported an average waiting time of 17 minutes. At 0.05 level of significance, what can you conclude about the restaurant's claim?
3. A psychologist claims that the attention span of Grade 11 students is 50 minutes. Thirty randomly selected students reported to have a mean of 46 minutes attention span. If the population standard deviation can be assumed to be 12 minutes, should the psychologist stick to his belief at 0.01 level of significance?
4. The mean weight of 20 packs of brand X detergent powder is 62.3 g with a standard deviation of 5g. However, the manufacturer claims that it contains an average of 65 g. Use 0.01 level of significance to validate the manufacturer's claim.
5. The owner of a café wants to know whether the true average number of customers that visit the store per day is 25. It is revealed that the average number of customers per day is 27 with a standard deviation of seven customers, in a random sample of 42 days. Is there enough evidence to reject the null at 0.05 level?
Directions: Identify the appropriate test statistic for each of the following, then justify your answer. (2 points each)
1. It is believed that the average monthly salary of a blogger is at least Php 100 000. A random sample of ten bloggers has shown an average monthly salary of Php 112 000 with a standard deviation of Php 15 000. At 0.01 level of significance, is the hypothesized mean true?
2. A new established restaurant in the city claims that the waiting time for customers is less than 15 minutes with a standard deviation of 2.5 minutes. Fifty randomly selected customers have reported an average waiting time of 17 minutes. At 0.05 level of significance, what can you conclude about the restaurant's claim?
3. A psychologist claims that the attention span of Grade 11 students is 50 minutes. Thirty randomly selected students reported to have a mean of 46 minutes attention span. If the population standard deviation can be assumed to be 12 minutes, should the psychologist stick to his belief at 0.01 level of significance?
4. The mean weight of 20 packs of brand X detergent powder is 62.3 g with a standard deviation of 5g. However, the manufacturer claims that it contains an average of 65 g. Use 0.01 level of significance to validate the manufacturer's claim.
5. The owner of a café wants to know whether the true average number of customers that visit the store per day is 25. It is revealed that the average number of customers per day is 27 with a standard deviation of seven customers, in a random sample of 42 days. Is there enough evidence to reject the null at 0.05 level?
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Answer:
1. The appropriate test statistic for this scenario is a one-sample t-test. We use a t-test when we want to test a hypothesis about a population mean, but the population standard deviation is unknown. In this case, we have a sample of salaries and we want to test whether the true average salary is at least Php 100,000. We use a one-sample t-test because we do not know the population standard deviation and we have a sample size of less than 30.
2. The appropriate test statistic for this scenario is a one-sample t-test. We use a t-test when we want to test a hypothesis about a population mean, but the population standard deviation is unknown. In this case, we have a sample of waiting times and we want to test whether the true average waiting time is less than 15 minutes. We use a one-sample t-test because we do not know the population standard deviation and we have a sample size of less than 30.
3. The appropriate test statistic for this scenario is a one-sample t-test. We use a t-test when we want to test a hypothesis about a population mean, but the population standard deviation is unknown. In this case, we have a sample of attention spans and we want to test whether the true average attention span is 50 minutes. We use a one-sample t-test because we do not know the population standard deviation and we have a sample size of less than 30.
4. The appropriate test statistic for this scenario is a one-sample t-test. We use a t-test when we want to test a hypothesis about a population mean, but the population standard deviation is unknown. In this case, we have a sample of weights and we want to test whether the true average weight is 65 g. We use a one-sample t-test because we do not know the population standard deviation and we have a sample size of less than 30.
5. The appropriate test statistic for this scenario is a one-sample t-test. We use a t-test when we want to test a hypothesis about a population mean, but the population standard deviation is unknown. In this case, we have a sample of daily customer numbers and we want to test whether the true average number of customers is 25. We use a one-sample t-test because we do not know the population standard deviation and we have a sample size of 42, which is greater than 30. However, we can also use a z-test because the sample size is large enough to assume a normal distribution.