Question

Does it take less time for seeds to germinate if they are near rock music that is continuously playing compared to being near classical music? The 42 seeds that were exposed to rock music took an average of 28 days to germinate. The standard deviation was 14 days. The 53 seeds that were exposed to classical music took an average of 34 days to germinate. The standard deviation for these seeds was 12 days. What can be concluded at the αα = 0.05 level of significance?

For this study, we should use Select an answer t-test for the difference between two independent population means t-test for the difference between two dependent population means t-test for a population mean z-test for the difference between two population proportions z-test for a population proportion

The null and alternative hypotheses would be:   

  

H0:H0:  Select an answer μ1 p1  Select an answer = < ≠ >  Select an answer p2 μ2  (please enter a decimal)   

H1:H1:  Select an answer p1 μ1  Select an answer > ≠ = <  Select an answer p2 μ2  (Please enter a decimal)

The test statistic ? z t  =  (please show your answer to 3 decimal places.)

The p-value =  (Please show your answer to 4 decimal places.)

The p-value is ? > ≤  αα

Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.

Thus, the final conclusion is that ...

The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population mean time for seeds exposed to rock music to germinate is less than the population mean time for seeds exposed to classical music to germinate.

The results are statistically insignificant at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time for seeds exposed to rock music to germinate is equal to the population mean time for seeds exposed to classical music to germinate.

The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population mean time for seeds exposed to rock music to germinate is less than the population mean time for seeds exposed to classical music to germinate.

The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the mean germination time for the 42 seeds exposed to rock music that were observed is less than the mean germination time for the 53 seeds that were exposed to classical music that were observed.

Interpret the p-value in the context of the study.

There is a 1.5% chance that the mean germination time for the 42 seeds exposed to rock music is at least 6 days less than the mean germination time for the 53 seeds exposed to classical music.

There is a 1.5% chance of a Type I error.

If the population mean time for seeds exposed to rock music to germinate is the same as the population mean time for seeds exposed to classical music to germinate and if another 42 seeds exposed to rock music and 53 seeds exposed to classical music are observed then there would be a 1.5% chance that the mean germination time for the 42 seeds exposed to rock music would be at least 6 days less than the mean germination time for the 53 seeds exposed to classical music.

If the mean germination time for the 42 seeds exposed to rock music is the same as the sample mean germination time for the 53 seeds exposed to classical music and if another 42 seeds exposed to rock music and 53 seeds exposed to classical music are observed then there would be a 1.5% chance of concluding that the mean germination time for the 42 seeds exposed to rock music is at least 6 days less than the mean germination time for the 53 seeds exposed to classical music

Interpret the level of significance in the context of the study.

If the population mean time for seeds exposed to rock music to germinate is the same as the population mean time for seeds exposed to classical music to germinate and if another 42 seeds exposed to rock music and 53 seeds exposed to classical music are observed, then there would be a 5% chance that we would end up falsely concuding that the sampe mean times to germinate for these 42 seeds exposed to rock music and 53 seeds exposed to classical music differ from each other.

There is a 5% chance that there is a difference in the population mean time for seeds exposed to rock vs. classical music to germinate.

If the population mean time for seeds exposed to rock music to germinate is the same as the population mean time for seeds exposed to classical music to germinate and if another 42 seeds exposed to rock music and 53 seeds exposed to classical music are observed then there would be a 5% chance that we would end up falsely concuding that the population mean time for seeds exposed to rock music to germinate is less than the population mean time for seeds exposed to classical music to germinate

There is a 5% chance that the seeds just don't like your taste in music, so please let someone else conduct the study.

Answer 1

Correct options are:

The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population mean time for seeds exposed to rock music to germinate is less than the population mean time for seeds exposed to classical music to germinate.

If the population mean time for seeds exposed to rock music to germinate is the same as the population mean time for seeds exposed to classical music to germinate and if another 42 seeds exposed to rock music and 53 seeds exposed to classical music are observed then there would be a 1.5% chance that the mean germination time for the 42 seeds exposed to rock music would be at least 6 days less than the mean germination time for the 53 seeds exposed to classical music.

If the population mean time for seeds exposed to rock music to germinate is the same as the population mean time for seeds exposed to classical music to germinate and if another 42 seeds exposed to rock music and 53 seeds exposed to classical music are observed then there would be a 5% chance that we would end up falsely concuding that the population mean time for seeds exposed to rock music to germinate is less than the population mean time for seeds exposed to classical music to germinate