Question Type 3: Performing a hypothesis test comparing two means of unpaired samples with equal variances Exercises

Two independent samples measure a new process yield (in %): Sample A ($n=5$): $12,15,14,10,13$; Sample B ($n=6$): $16,18,17,19,20,22$. Assuming equal variances, test at the 5% level whether the mean yields differ.

A factory measures product weight before and after calibration on 6 items (g): $(50.2,50.1),(49.8,49.7),(50.5,50.4),(50.0,49.9),(50.3,50.1),(49.9,49.8)$. At the 5% level, test whether calibration changes the mean weight.

Seven patients had blood pressure measured before and after a new drug: $(8.1,7.5),(7.8,7.7),(8.5,8.0),(7.9,7.4),(8.2,7.9),(8.0,7.6),(7.7,7.2)$ (units kPa). At the 5% level, test whether the drug significantly lowers blood pressure.

Ten students took a test before and after a review session. Scores (before, after): $(70,75),(65,70),(80,85),(60,65),(75,80),(85,90),(55,60),(90,92),(78,83),(68,74)$. At the 1% level, test if the review session improved scores.

Eight pairs of athletes had running times measured on grass and synthetic track (s): $(12.1,11.8),(11.9,11.7),(12.4,12.0),(12.0,11.6),(12.2,11.9),(12.3,11.8),(11.8,11.5),(12.5,12.1)$. At the 5% level, test whether synthetic track yields faster times (assume paired).

Perform a hypothesis test at the 5% significance level to determine if the mean calorie consumption differs between viewers of horror and romance films. The horror‐film sample (in calories) is: $345,234,45,216,543,143,576,396$. The romance‐film sample is: $453,112,887,593,953,438,299,548,671$. Assume the two populations have equal variances.

A group of 10 people each watched a horror film and a romance film. Their calorie consumption (horror, romance) are: $(345,453),(234,112),(45,887),(216,593),(543,953),(143,438),(576,299),(396,548),(222,671),(341,554)$. At the 5% level, test whether the mean consumption differs between the two film genres.

Two machines produce metal rods. Sample lengths (mm): Machine 1 ($n=10$): $100.5,101.0,99.8,100.2,100.9,101.1,100.4,100.0,99.9,100.7$; Machine 2 ($n=12$): $100.1,100.3,99.7,100.2,100.5,99.8,100.0,100.4,100.2,99.9,100.6,100.8$. Test at 5% whether the mean lengths differ, assuming equal variances.

At the 1% level, compare the mean speeds (km/h) of two cycling training programs: Program A ($n=9$): $30,32,31,29,33,34,30,31,32$; Program B ($n=9$): $28,29,27,30,29,28,31,27,30$. Assume equal variances.

At the 1% level, test whether two battery brands differ in mean lifetime. Brand A ($n=7$): $200,210,190,205,215,195,220$ (hours); Brand B ($n=8$): $180,175,185,170,190,200,195,205$. Assume equal variances.