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Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is µ = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than µ = 19 inches? Use ???? = 0.05.

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Cricetus

Answer:

The test statistics will be "-0.876",

Step-by-step explanation:

Given:

  • [tex]\bar x=18.6[/tex]
  • [tex]\mu = 19[/tex]
  • [tex]s = 3.1[/tex]
  • [tex]n = 46[/tex]

According to the question,

Level of significance will be:

= 0.05

Now,

The test statistics will be:

= [tex]\frac{\bar x-\mu}{\frac{s}{\sqrt{n} } }[/tex]

By substituting the values, we get

= [tex]\frac{18.6-19}{\frac{3.1}{\sqrt{46} } }[/tex]

= [tex]-\frac{2.713}{3.1}[/tex]

= [tex]-0.876[/tex]

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