## DESCRIPTION ## Match each of the following hypothesis tests with their corresponding descriptions. ## ENDDESCRIPTION ## KEYWORDS('hypothesis tests','descriptions') ## DBsubject('Biostatistics') ## DBchapter('') ## DBsection('') ## Date('2026-07-12') ## Author('Neil R. Voss') ## Institution('Roosevelt University') DOCUMENT(); loadMacros( 'PGstandard.pl', 'PGML.pl', 'PGchoicemacros.pl', 'parserPopUp.pl', 'parserUtils.pl', 'PGgraders.pl', 'PGcourse.pl' ); our @ALPHABET = ('A' .. 'Z'); # ================================ # Full matching data # ================================ %match_data = ( 'Benchmark Z-test' => [ 'Compares the mean of a sample to a known population mean when the population variance is known.', 'Used when comparing a sample\'s mean to a large dataset with a known population standard deviation.', 'The population mean systolic blood pressure is 120 mmHg with a standard deviation of 3.9 mmHg. You are testing a sample of n = 100 patients to see if the mean blood pressure differs from 120 mmHg.', 'The population mean gene expression is 200 units with a standard deviation of 5 units. You have a sample of n = 150 treated cells and want to test if the mean gene expression differs from the population mean.', 'The population mean pH in a wetland is 7.5 with a standard deviation of 0.32. You are sampling n = 50 water samples to check if the average pH has changed over time.', 'The average heart rate of a healthy adult population is 72 bpm, with a standard deviation of 4 bpm. You have a sample of n = 50 patients and want to test if their average heart rate differs from the population mean.', 'In a population of bacteria, the average gene expression level for a key metabolic gene is 100 units, with a standard deviation of 6 units. You collect n = 40 treated bacterial samples and want to test if their gene expression level differs from the population mean.', 'The average temperature in a coastal region is 20°C, with a standard deviation of 1.5°C. You collect n = 35 daily temperature readings from a nearby estuary and want to test if the estuary\'s average temperature differs from the regional mean.', ], 'Benchmark T-test' => [ 'Compares the mean of a sample to a known population mean when the population variance is unknown.', 'Used when the population variance is unknown, and you have a smaller sample size (n < 30).', 'The population mean resting heart rate is 70 bpm, but the standard deviation is unknown. You collect a sample of n = 25 patients on a new drug to test if their mean heart rate differs from the population mean.', 'The population mean protein concentration is 50 mg/mL, but the standard deviation is unknown. You are working with n = 20 samples and want to test if the mean protein concentration differs from the known mean.', 'The population mean species richness is 25 species per plot, but the standard deviation is unknown. You have a small sample of n = 18 plots and want to test if species richness differs from the population mean.', 'The average blood sugar level in the population is 90 mg/dL, but the standard deviation is unknown. You collect a sample of n = 20 patients and want to test if their average blood sugar level differs from the population mean.', 'The average protein concentration in a standard cell line is 50 mg/mL, but the standard deviation is unknown. You collect n = 15 samples from a modified cell line to test if the mean protein concentration differs from the standard.', 'The average tree height in a natural forest is 12 meters, but the standard deviation is unknown. You collect n = 12 samples from a reforested area to test if the average tree height differs from the natural forest.', ], 'Two-Sample T-test' => [ 'Compares the means of two independent groups to determine if they are statistically different from each other.', 'Used to determine whether the average heights of two different plant species are significantly different.', 'You are comparing the mean cholesterol levels between two groups, one receiving a placebo and the other a treatment. Each group contains n = 20 participants. You want to test if the means are significantly different.', 'You are comparing the mean gene expression of two cell lines, one treated and one untreated, with n = 25 samples in each group. You want to test if the means are significantly different.', 'You want to test if the mean number of species differs between two regions, one pristine and one affected by deforestation, with n = 25 plots in each region.', 'You are comparing the average recovery times between two groups of patients, one receiving a new drug and one receiving standard care, with n = 25 patients in each group. You want to test if the means are different.', 'You are comparing the average enzyme activity between two experimental conditions, one treated with a new inhibitor and one with a control, with n = 20 samples in each group. You want to test if the means are different.', 'You want to compare the average soil pH between two agricultural fields, one using organic fertilizer and one using conventional methods, with n = 30 soil samples from each field. You want to test if the means are significantly different.', ], 'Two-Sample F-test' => [ 'Compares the variances of two independent groups to test if the variability between them is significantly different.', 'Used to test whether two different batches of products have equal variability in their measurements.', 'You are comparing the variability in blood pressure between two groups, one with n = 25 patients on a standard drug and another with n = 40 patients on an experimental drug. You want to test if the variances are different.', 'You are comparing the variance of protein concentrations between two experimental batches, each with n = 25 samples, to see if their variability differs.', 'You are comparing the variability in soil nutrient levels between two areas, one fertilized and one unfertilized, with n = 25 samples in each group. You want to test if the variances differ.', 'You are comparing the variability in cholesterol levels between two groups, one receiving a diet plan and the other receiving medication, with n = 40 patients in each group. You want to test if the variances are significantly different.', 'You are comparing the variability in protein yield between two different laboratory protocols, each using n = 25 samples. You want to test if the variances in protein yield are significantly different.', 'You are comparing the variability in air pollution measurements between two cities, with n = 35 measurements from each city. You want to test if the variances in pollution levels differ significantly.', ], 'Analysis of Variance (ANOVA)' => [ 'Compares the means of more than two groups to determine if at least one group\'s mean is significantly different from the others.', 'Used to compare the average exam scores across three different classrooms.', 'You want to compare the mean blood glucose levels of patients in four drug groups, each group has n = 30 participants. You want to test if at least one group\'s mean differs significantly.', 'You are testing if the mean protein abundance differs across four experimental conditions, with n = 25 samples per condition.', 'You want to compare the mean number of plant species across five habitats, with n = 20 plots in each habitat. You want to test if any habitat shows a significantly different mean.', 'You want to compare the mean weight loss between patients following four (4) different diet plans, with n = 30 participants in each group. You want to test if there are significant differences in mean weight loss across the groups.', 'You are testing if the mean DNA replication rate differs across four different temperatures, with n = 20 samples per temperature. You want to test if any group shows significantly different replication rates.', 'You are studying bird populations across five different habitats. You collect n = 25 bird counts from each habitat and want to test if there is a significant difference in the mean number of birds observed across the habitats.', ], ); # ------------------------------- # Select N random keys # ------------------------------- my $n = 5; @all_keys = PGsort(sub { $_[0] lt $_[1] }, keys %match_data); my $local_seed = (defined($problemSeed) && $problemSeed ne '') ? $problemSeed : 1; my $local_random = new PGrandom($local_seed); my @indices = (0 .. $#all_keys); my @shuffled = (); while (@indices) { my $pick = $local_random->random(0, $#indices, 1); push @shuffled, splice(@indices, $pick, 1); } my @selected_keys = @all_keys[@shuffled[0..$n-1]]; # ------------------------------- # Build question/answer pairs # ------------------------------- # Each entry: [prompt, choice] @q_and_a = (); foreach my $key (@selected_keys) { my $values_ref = $match_data{$key}; my $i = $local_random->random(0, $#$values_ref, 1); my $value = $values_ref->[$i]; push @q_and_a, [ $value, $key ]; } # ------------------------------- # Randomize the questions # ------------------------------- my @q_indices = (0 .. $#q_and_a); my @q_shuffled = (); while (@q_indices) { my $pick = $local_random->random(0, $#q_indices, 1); push @q_shuffled, $q_and_a[splice(@q_indices, $pick, 1)]; } @q_and_a = @q_shuffled; # ------------------------------- # Sort the choices alphabetically # ------------------------------- @answers = (); push(@answers, (map { $_->[1] } @q_and_a)); @answers_sorted = PGsort(sub { $_[0] lt $_[1] }, @answers); # ------------------------------- # HTML-safe answer labels # ------------------------------- %answer_html = ( 'Benchmark Z-test' => 'Benchmark Z-test', 'Benchmark T-test' => 'Benchmark T-test', 'Two-Sample T-test' => 'Two-Sample T-test', 'Two-Sample F-test' => 'Two-Sample F-test', 'Analysis of Variance (ANOVA)' => 'Analysis of Variance (ANOVA)', ); @answers_sorted_html = map { $answer_html{$_} || $_ } @answers_sorted; # ------------------------------- # Create answer index lookup # ------------------------------- our %answer_index; for (my $i = 0; $i <= $#answers_sorted; $i++) { $answer_index{$answers_sorted[$i]} = $i; } # ------------------------------- # PopUp/DropDown compatibility # ------------------------------- sub make_popup { return defined &DropDown ? DropDown(@_) : PopUp(@_); } # ------------------------------- # Create popup objects (blank default) # ------------------------------- my @answer_letters = @ALPHABET[0 .. $#answers_sorted]; my @answer_letters_with_blank = ('', @answer_letters); @answer_dropdowns = map { make_popup([ @answer_letters_with_blank ], $answer_index{$q_and_a[$_][1]} + 1 ) } 0 .. $#q_and_a; # ------------------------------- # Render the question # ------------------------------- HEADER_TEXT(< .pgml-bold { font-weight: 700; } .two-column { display: flex; flex-wrap: wrap; gap: 2rem; align-items: center; justify-content: space-evenly; } END_STYLE $question_text = 'Match each of the following hypothesis tests with their corresponding descriptions.'; $note_text = 'Note: Each choice will be used exactly once.'; BEGIN_PGML [$question_text]* [$note_text]* [@ MODES(HTML => '

') @]* [@ join( "\n\n", map { '[_]{$answer_dropdowns[' . $_ . ']} ' . '*' . ($_ + 1) . '.* ' . '[$q_and_a[' . $_ . '][0]]*' } 0 .. $#q_and_a ) @]** [@ MODES(HTML => '

') @]* [@ join( "\n\n", map { chr(65 + $_) . '\\.' . ' ' . '[$answers_sorted_html[' . $_ . ']]*' } 0 .. $#answers_sorted ) @]** [@ MODES(HTML => '

') @]* END_PGML # ------------------------------- # Dynamic Partial Credit Based on $n # ------------------------------- $showPartialCorrectAnswers = 0; my @thresholds; my @scores; for (my $i = 1; $i <= $n; $i++) { push @thresholds, $i; push @scores, sprintf("%.2f", $i / $n); } install_problem_grader(~~&custom_problem_grader_fluid); $ENV{grader_numright} = [@thresholds]; $ENV{grader_scores} = [@scores]; $ENV{grader_message} = 'You can earn partial credit.'; # ------------------------------- # Solution # ------------------------------- $answer_list = join(', ', map { ($_ + 1) . '-' . $ALPHABET[$answer_index{$q_and_a[$_][1]}] } 0 .. $#q_and_a); BEGIN_PGML_SOLUTION The correct answers are: [$answer_list]. END_PGML_SOLUTION ENDDOCUMENT();