O Alternative hypothesis states: female population variance > a. male population variance O Alternative hypothesis states: female population variance < male population variance O Alternative hypothesis states: female population mean > male population mean O Alternative hypothesis states: female population mean < male population mean b. What is the critical value for this test? c What is the test statistic for this test?

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A biologist who studies spiders believes that not only do female green lynx spiders tend to be longer than their male counterparts but also that the lengths of the females vary more than those of the male spiders. To investigate the latter (second) belief, she obtained a random sample of 9 male spiders which yielded a mean length of 6.828 cm and a standard deviation of 0.617 cm as well as a random sample of 10 female spiders which yielded a mean length of 8.917 cm and a standard deviation of 1.27 cm. Do the data support the biologist’s claim if a significance level of 5% is used?

Let X be the length of the male spiders and let Y be the length of the female spiders.

Complete the following by providing the values requested and selecting the most appropriate option, where applicable.

 

 

O Alternative hypothesis states: female population variance >
a.
male population variance
O Alternative hypothesis states: female population variance <
male population variance
O Alternative hypothesis states: female population mean >
male population mean
O Alternative hypothesis states: female population mean <
male population mean
b. What is the critical value for this test?
c. What is the test statistic for this test?
d. O Decision: Do Not Reject the null hypothesis
O Decision: Reject the null hypothesis
O At a significance level of 5% there is insufficient evidence to
е.
conclude that the data supports the biologist's claim that the
lengths of female green lynx spiders vary more than those of
male green lynx spiders
O At a significance level of 5% there is sufficient evidence to
conclude that the data supports the biologist's claim that the
lengths of female green lynx spiders vary more than those of
male green lynx spiders
O At a significance level of 5% there is insufficient evidence to
conclude that the data supports the biologist's claim that the
lengths of female green lynx spiders are longer than those of
male green lynx spiders
O At a significance level of 5% there is sufficient evidence to
conclude that the data supports the biologist's claim that the
lengths of female green lynx spiders are longer than those of
male green lynx spiders
Transcribed Image Text:O Alternative hypothesis states: female population variance > a. male population variance O Alternative hypothesis states: female population variance < male population variance O Alternative hypothesis states: female population mean > male population mean O Alternative hypothesis states: female population mean < male population mean b. What is the critical value for this test? c. What is the test statistic for this test? d. O Decision: Do Not Reject the null hypothesis O Decision: Reject the null hypothesis O At a significance level of 5% there is insufficient evidence to е. conclude that the data supports the biologist's claim that the lengths of female green lynx spiders vary more than those of male green lynx spiders O At a significance level of 5% there is sufficient evidence to conclude that the data supports the biologist's claim that the lengths of female green lynx spiders vary more than those of male green lynx spiders O At a significance level of 5% there is insufficient evidence to conclude that the data supports the biologist's claim that the lengths of female green lynx spiders are longer than those of male green lynx spiders O At a significance level of 5% there is sufficient evidence to conclude that the data supports the biologist's claim that the lengths of female green lynx spiders are longer than those of male green lynx spiders
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