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Question 1: A random sample of 22 observations taken from a population that is normally distributed produced a sample mean of 58.5 and a standard deviation of 7.5.

Find the range for the *p*-value and the critical and observed values of *t* for the following test of hypothesis, using α = 0.01 .

H 0 : μ = 55 versus H 1 : μ > 55 .

Use the *t* distribution table to find a range for the *p*-value.

Question 2:

A random sample of 19 observations taken from a population that is normally distributed produced a sample mean of 42.4 and a standard deviation of 8. Find the range for the *p*-value and the critical and observed values of *t* for each of the following tests of hypotheses using, α = 0.01 .

Use the *t* distribution table to find a range for the *p*-value.

Round your answers for the values of *t* to three decimal places.

**a.** H 0 : μ = 46 versus H 1 : μ < 46 .

Enter your answer; the range for the p-value for the item a) of the question statement, lower bound < *p*-value <Enter your answer; the range for the p-value for the item a) of the question statement, upper bound

t _{critical} | =Enter your answer; t_critical |

t _{observed} | =Enter your answer; t_observed |

Question 3:

A random sample of 550 observations produced a sample proportion equal to 0.36. Find the critical and observed values of *z* for the following test of hypotheses using α = 0.02 .

H 0 : p = 0.30 versus H 1 : p ≠ 0.30 .

Round your answers to two decimal places.

*z* _{critical left} =Enter your answer; z_critical left

*z* _{critical right} =Enter your answer; z_critical right

*z* _{observed} =

**b.** H 0 : μ = 46 versus H 1 : μ ≠ 46 .

Enter your answer; the range for the p-value for the item b) of the question statement, lower bound < *p*-value <Enter your answer; the range for the p-value for the item b) of the question statement, upper bound

t _{critical left} | =Enter your answer; t_critical left |

t _{critical right} | =Enter your answer; t_critical right |

t _{observed} |

Round your answers for the values of *t* to three decimal places.

Enter your answer; the range for the p-value, lower bound < *p*-value <Enter your answer; the range for the p-value, upper bound

*t* _{critical} =Enter your answer; t_critical

*t* _{observed} =Enter your answer; t_observed

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