Statistics and Probability

It is an assertion or a claim about a population parameter that suggests neutrality between variables.

• alternative hypothesis

• directional hypothesis

• inductive hypothesis

• null hypothesis

Which of the following statements is true?

• Type II error is committed if the null hypothesis is true and accepted.

• Type I error is committed if the null hypothesis is true and accepted.

• Type II error is committed if the null hypothesis is true and rejected.

• Type I error is committed if the null hypothesis is true and rejected.

A bakery shop owner claims that the mean sale of his special bread is 1500 pieces per day. Determine the parameter to be tested in the given problem.

• The special bread.

• The bakery shop owner.

• Number of pieces of bread sold in a day

• Mean sales of the special bread per day.

.A hospital claims that only 5% of its patients are unhappy with the attention they have received. Identify the parameter to be tested in the given problem.

• Care that the hospital can provide.

• Percentage of the patients in the hospital.

• Proportion of unhappy patients in the hospital.

• Patients who are happy with the services of the hospital.

A clinical psychologist asserts that the average attention span of a 12-year-old is about 30 minutes. This is against the recorded attention span which is about 40 minutes. What is the appropriate null hypothesis for this claim?

• The average attention span can be longer than 30 minutes.

• A 12-year-old student has an average attention span of 30 minutes.

• A 12-year-old student cannot focus on a task for about 30 minutes.

• The average attention span of a 12-year-old student is less than 30 minutes

Mr. Abad claims that his students performed better in the fourth quarter than the previous quarter based on the results of their quarter examination. The mean score of his students in the fourth quarter is greater than 40 points. Which of the following is the appropriate alternative hypothesis if a one-tailed test with a 0.05 level of significance?

• The mean score of the students in their fourth quarter examination is the same as their mean score in the third quarter.

• The mean score of the students in their fourth quarter examination is not equal to their mean score in the third quarter

• The mean score of the students in their fourth quarter examination is greater than their mean score in the third quarter.

• The mean score of the students in their fourth quarter examination is less than their mean score in the third quarter.

A researcher believes that the average cost of a Statistics workbook is PHP 180. She samples 30 workbooks and calculates the mean of the sample to be PHP 205. Does this value warrant the conclusion that the average cost of workbooks is greater than PHP 180?

• The mean population might be higher than PHP 180.

• The true average of the population of all workbooks might indeed be PHP 180.

• No, there is insufficient information. The population might be lower than PHP 180.

• No, there is insufficient information. The population might be larger than PHP 180.

If the sample size is large (𝑛 ≥ 30), or when the population is normally distributed with known population variance, what test statistic for one sample group is appropriate to use?

• one-sample t-test

• one-sample z-test

• Pearson r

• . Linear Regression

The school nurse of a public school in Pampanga claims that the mean weight of grade 11 students is 55.6 kg with a standard deviation of 5.4 kg. The HOPE teacher takes a random sample of 35 STEM students and found out to have a mean weight of PHP 52.3 kg. To test the claim of the teacher with a level of significance of 0.05, what test statistic is appropriate to use assuming the data came from a normal distribution?

• one-sample t-test

• one-sample z-test

• Pearson r

• Linear Regression

A social worker in a barangay claim that the mean monthly salary of the families in their barangay is Php 21,750 with a standard deviation of Php 16,000. A researcher takes a random sample of 25 families, who are found to have a mean salary of Php 19,875. Is the sample size large enough for the central limit theorem to apply?

• Yes, since n = 25 the central limit theorem applies.

• Yes, since n = 0.05 the central limit theorem applies.

• No, since n = 25 the central limit theorem cannot be applied.

• No, since the n = 0.05 the central limit theorem cannot be applied.