Question

The recommended daily dietary allowance for zinc among males
older than age 50 years is 15 mg/day. An article reports the
following summary data on intake for a sample of males age 65−74
years: *n* = 115, *x* = 12.1, and *s* = 6.57.
Does this data indicate that average daily zinc intake in the
population of all males age 65−74 falls below the recommended
allowance? (Use *α* = 0.05.)

*H*_{0}: μ = 15

*H*_{a}: μ < 15

Calculate the test statistic and determine the *P*-value.
(Round your test statistic to two decimal places and your
*P*-value to four decimal places.)

z | =? | |

P-value | =? |

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer #1

Solution :

Given that,

Population mean = = 15

Sample mean = = 12.1

Population standard deviation = = 6.57

Sample size = n = 115

Level of significance = = 0.05

The test statistics,

Z =( - )/ (/n)

= ( 12.1 - 15 ) / ( 6.57 / 115)

= -4.73

p-value = P(Z < z )

= P(Z < -4.73)

= 0

The p-value is p = 0, and since p = 0 < 0.05, it is concluded that the null hypothesis is rejected.

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