Question

A sample of *n* = 16 individuals is randomly selected
from a population with a mean of *μ* = 65, and a treatment
is administered to the individuals in the sample. After treatment,
the sample mean is found to be *M* = 73.

(a) If the sample standard deviation is *s* = 11, are the
data sufficient to conclude that the treatment has a significant
effect using a two-tailed test with *α* = 0.05? (Round your
answers to three decimal places.)

t-critical = |
± | |

t = |

(b) If the sample standard deviation is *s* = 18, are the
data sufficient to conclude that the treatment has a significant
effect using a two-tailed test with *α* = 0.05? (Round your
answers to three decimal places.)

t-critical = |
± | |

t
= |

Answer #1

df = n-1 = 16 - 1 = 15

a )

t critical = 2.131

t = M - / S / sqrt(n)

= 73 - 65 / 11 / sqrt(16)

= 2.909

Since test statistics falls in rejection region, Reject the null hypothesis

We conclude that we have sufficient evidence to support the claim.

b)

t critical = 2.131

t = M - / S / sqrt(n)

= 73 - 65 / 18 / sqrt(16)

= 1.778

Since test statistics falls in non-rejection region, Do not reject the null hypothesis

We conclude that we have insufficient evidence to support the claim.

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