A manufacturer's association claims that 92% of adults own cell phones. A technology researcher thinks the...

A manufacturer's association claims that 92% of adults own cell phones. A technology researcher thinks the proportion is lower. In a random sample of 300 adults, 267 said they had a cell phone. Using these results and a 0.05 significance level, formulate and test the researcher's hypothesis.

Ho=

Ha=

Sample Statistic =

null value =

SE =

Z statistic =

Test type =

p-value =

Decision =

Expert Solution

Ho :   p =    0.92
H1 :   p <   0.92       (Left tail test)

Level of Significance,   α =    0.05
Number of Items of Interest,   x =   267
Sample Size,   n =    300

Sample Proportion ,    p̂ = x/n =    0.89

Standard Error ,    SE = √( p(1-p)/n ) =    0.0157
Z Test Statistic = ( p̂-p)/SE = (   0.8900   -   0.92   ) /   0.0157   =   -1.9153


p-Value   =   0.027725395   [excel function =NORMSDIST(z)]
Decision:   p-value<α , reject null hypothesis

There is enough evidence to support the claim that proportion is lower

Please revert back in case of any doubt.

Please upvote. Thanks in advance.

orchestra answered 3 years ago

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