Question

The Student's *t* distribution table gives critical
values for the Student's *t* distribution. Use an
appropriate *d.f.* as the row header. For a
*right-tailed* test, the column header is the value of
*α* found in the *one-tail area* row. For a
*left-tailed* test, the column header is the value of
*α* found in the *one-tail area* row, but you must
change the sign of the critical value *t* to −*t*.
For a *two-tailed* test, the column header is the value of
*α* from the *two-tail area* row. The critical values
are the ±*t* values shown.

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 51
fish caught, the mean length was *x* = 18.4 inches, with
estimated standard deviation *s* = 2.8 inches. Do these data
indicate that the average length of a trout caught in Pyramid Lake
is less than *μ* = 19 inches? Use *α* = 0.05. Solve
the problem using the critical region method of testing (i.e.,
traditional method). (Round the your answers to three decimal
places.)

test statistic | = | |

critical value | = |

Answer #1

To test against

Here

sample mean

sample standard deviation

and sample size n = 51

The test statistic can be written as

which under H_{0} follows a t distribution with n-1 df.

We reject H_{0} at 5% level of significance if

Now,

The value of the test statistic =

and critical value

Since
, so we fail to reject H_{0} at 5% level of significance
and we can conclude that the average length of a trout caught in
Pyramid Lake is not significantly less than 19 inches.

The Student's t distribution table gives critical values for the
Student's t distribution. Use an appropriate d.f. as the row
header. For a right-tailed test, the column header is the value of
α found in the one-tail area row. For a left-tailed test, the
column header is the value of α found in the one-tail area row, but
you must change the sign of the critical value t to −t. For a
two-tailed test, the column header is the value...

The Student's t distribution table gives critical values for the
Student's t distribution. Use an appropriate d.f. as the row
header. For a right-tailed test, the column header is the value of
α found in the one-tail area row. For a left-tailed test, the
column header is the value of α found in the one-tail area row, but
you must change the sign of the critical value t to −t. For a
two-tailed test, the column header is the value...

The Student's t distribution table gives critical values for the
Student's t distribution. Use an appropriate d.f. as the row
header. For a right-tailed test, the column header is the value of
α found in the one-tail area row. For a left-tailed test, the
column header is the value of α found in the one-tail area row, but
you must change the sign of the critical value t to −t. For a
two-tailed test, the column header is the value...

The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail arearow. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value of...

11) The Student's t distribution table gives critical values for
the Student's t distribution. Use an appropriate d.f. as the row
header. For a right-tailed test, the column header is the value of
α found in the one-tail area row. For a left-tailed test, the
column header is the value of α found in the one-tail area row, but
you must change the sign of the critical value t to −t. For a
two-tailed test, the column header is the...

The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
? found in the one-tail area row. For a
left-tailedtest, the column header is the value of
? found in the one-tail area row, but you must
change the sign of the critical value t to ?t.
For a two-tailed test, the column header is the value of...

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