Question

A random sample of *n* = 1,300 observations from a
binomial population produced *x* = 618.

(a) If your research hypothesis is that *p* differs from
0.5, what hypotheses should you test?

*H*_{0}: *p* ≠ 0.5 versus
*H*_{a}: *p* = 0.5 *H*_{0}:
*p* < 0.5 versus *H*_{a}: *p* >
0.5 *H*_{0}: *p* =
0.5 versus *H*_{a}: *p* > 0.5
*H*_{0}: *p* = 0.5 versus
*H*_{a}: *p* < 0.5 *H*_{0}:
*p* = 0.5 versus *H*_{a}: *p* ≠
0.5

(b) Calculate the test statistic and its *p*-value. (Round
your test statistic to two decimal places and your *p*-value
to four decimal places.)

z |
= |

p-value |
= |

Use the *p*-value to evaluate the statistical significance
of the results at the 1% level.

*H*_{0} is not rejected since the
*p*-value is not less than 0.01. *H*_{0} is
rejected since the *p*-value is not less than
0.01. *H*_{0} is not
rejected since the *p*-value is less than 0.01.
*H*_{0} is rejected since the *p*-value is
less than 0.01.

(c) Do the data provide sufficient evidence to indicate that
*p* is different from 0.5?

Yes, the data provide sufficient evidence to indicate that
*p* is different from 0.5. No, the data do not provide
sufficient evidence to indicate that *p* is different from
0.5.

Answer #1

Solution :

Given that,

= 0.5

1 - = 0.5

n =1300

x = 618

Point estimate = sample proportion = = x / n = 0.475

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.5

Ha: p 0.5

Test statistics

z = ( - ) / *(1-) / n

= ( 0.475 - 0.5) / (0.5*0.5) / 1300

**= -1.775**

P-value = 2 * P(Z < z )

= 2 * P(Z < -1.775 )

= 2 * 0.0379

**= 0.9621**

Since , P-value > 0.01, fail to reject .

**No, the data do not provide sufficient evidence to
indicate that p is different from 0.5.**

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