Question

Consider testing Upper H 0 : mu equals 20H0: μ=20 against Upper H Subscript a Baseline : mu less than 20Ha: μ<20 where muμ is the mean number of latex gloves used per week by all hospital​employees, based on the summary statistics nequals=444, x overbarxequals=19.3 and sequals=11.1 Complete parts a and b.

Answer 1

Test:
`\mu` < 20 with normal distⁿ

Hypothesis test:

H0:
`\mu \ge` 20 (Null Hypothesis, H₀ :
`\mu` = 20 is also correct)

H1:
`\mu` < 20 (Alternative Hypothesis, also called H₁)

This is lower tailed test.

Since sample is large, sample standard deviation can be taken as an approximation of population standard deviation.

x = 19.3

`\sigma` = 11.1

n = 444

significance level,
`\alpha` = 0.05 (If no value is given, we take level of 0.05)

Test statistic
`z* = (x-\mu)/(\sigma/√(n))`

`= (19.3-20)/(11.1/√(444))`

= - 1.33

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